luxury apartments / penthouses with panoramic view for rent International (page 4)

In the heart of the Place des Victoires, on the main floor of a private mansion built in the late 17th century—a listed historic monument overlooking one of Paris’s most elegant royal squares—we are pleased to present an apartment with exceptional architectural and historical features. Notably, it was once home to the wealthiest man in France during the reign of Louis XIV, whose statue stands proudly in the center of this iconic square. The apartment consists of a double reception room spanning nearly 100 m², featuring spectacular double-height ceilings, Versailles-style parquet floors, fireplaces, moldings, and a wrap-around balcony offering breathtaking views of the square. It also includes a semi-professional kitchen, a laundry room, and two bedrooms, each with its own bathroom, including a spacious 53 m² master suite with a walk-in closet and an en-suite bathroom. The apartment is accessible by elevator and features built-in air conditioning in every room, central heating, and double-glazed windows. The bedrooms are equipped with electric roller shutters that provide complete privacy. This location offers a unique living environment steeped in history, just a short walk from the Palais-Royal, the Louvre, the Opera, and the capital’s most exclusive spots, while enjoying the tranquility and prestige of one of Paris’s most beautiful squares. A basement storage unit and a nearby parking space—offered at an additional cost—complete this exceptional property. Lease available only under the Civil Code. The lease term can be a minimum of 3 months or longer, with or without tacit renewal.

Avenue de New York. This beautifully appointed duplex apartment rented furnished is on the 6th and top floor of a fine early 20th century freestone building. Featuring high ceilings and commanding exceptional views of the Eiffel Tower, it offers 215 sqm of living space including a spacious living/reception room and dining room bathed in sunshine, a fully fitted and equipped kitchen, a master suite with a bath/shower room/wc and dressing room, two bedrooms with a mezzanine, a shower room and two separate wc. Upstairs a study/TV lounge with a shower room and a separate wc opens onto a roof terrace commanding exceptional views of the capital. With a parking space and a cellar. Available exclusively under the conditions of the code Civil. Information regarding the environment is available on http://www.georisques.gouv.fr

AVAILABLE OCT 26 Barnes presents this unique penthouse on Madrid’s Gran Vía — a true privilege in the heart of the city. What truly sets it apart, beyond its location, is the natural light that floods every corner, thanks to large windows and high ceilings, creating a warm and welcoming atmosphere from the very first moment. It features two private terraces with direct access from the living area — perfect for enjoying panoramic views of the city or simply relaxing outdoors in your own private space. The apartment offers two bedrooms and two full bathrooms, a fully equipped kitchen, a living-dining area, and terraces that are the true highlights of the home. It comes fully furnished and equipped, with a carefully designed interior and everything you need to move in effortlessly. It also includes a home automation system, underfloor heating, and all modern comforts, set in a classic building that was fully renovated in 2022. Residents also enjoy 24-hour concierge service, a gym, solarium, and an impressive communal rooftop terrace. Available for stays of a minimum of 6 months .

Experience elevated Miami living at Casa Bella Residences by B&B Italia. Perched on the 43rd floor, this exceptional 3-bedroom plus den, 3.5-bath residence is one of only five of this size in the building, offering 2,823 SF plus a 329 SF east-facing terrace. Floor-to-ceiling glass frames sweeping views of Biscayne Bay, PortMiami and the Miami skyline. Sophisticated interiors showcase Italian cabinetry, integrated Wolf & Sub-Zero appliances, elegant stone finishes and exceptional attention to detail. High-end custom walk-in closets will be completed prior to lease commencement. Two assigned parking spaces included. Amenities include two pools, including a rooftop pool, fitness center, spa, yoga & Pilates studios, café, business center, movie theater and private dining.

“Peninsula Terrace is the fresh new modern face of Bayonne, its prime location, neighborhood feel, and style set it apart completely from the other buildings in Bayonne. The intimate building is in the heart of Bayonne on the corner of 30th Street and Avenue C. It’s minutes from the 34th Street Light Rail station and is serviced directly by the NJ Transit bus lines to Exchange Place, the Port Authority Bus Terminal, and Lower Manhattan. The building features parking for all residents, a fitness center, and a breathtaking rooftop deck with 360-degree views of Bayonne and the New York City skyline. The building is entirely keyless entry and features high security standards. Peninsula Terrace also features a ButterflyMX intercom system, which allows residents to see and screen their guests arriving remotely from their smartphones. The units include condo level finishes and features. Each unit has a gas range stove, full-size washer and dryer, quartz counter tops, and central air conditioning. The apartments have solid core doors and additional insulation for superior sound control. Our 1 line has extra large master bedrooms. Watch fabulous sunsets from this top floor gem! Bayonne is 30 minutes from Manhattan and 1 hour from the Jersey Shore.

Ideally located on the prestigious Avenue de Tervuren in Woluwe-Saint-Pierre, on the 7th floor of a contemporary building, this elegant apartment offers a surface area of approximately 125 sqm and a generous 25 sqm terrace. The property is offered as a short-term furnished rental, available immediately until 30 November 2026. The apartment stands out for its spacious proportions, abundant natural light and comfortable layout. It comprises an entrance hall leading to a spacious living room of approximately 45 sqm with access to the terrace, as well as a fully equipped open-plan kitchen of approximately 14.5 sqm. The night area features two bedrooms of approximately 15.5 sqm and 11.5 sqm, a bathroom, a shower room and a night hall. A laundry room and additional storage spaces complete the property. Outside, the approximately 25 sqm terrace provides a pleasant extension of the living and reception areas. The apartment benefits from double glazing, a mechanical ventilation system and collective gas heating with a condensing boiler. The EPC report indicates an energy rating of B- and an EPC surface area of 121.47 sqm. A contemporary property enjoying a sought-after address in Woluwe-Saint-Pierre, within easy reach of shops, public transport and green spaces. EPC: B- EPC reference: 5ae8-e977-8430-289a EPC surface area: 121.47 sqm

Real Estate Passion - PARIS presents: A prestigious address in the La Muette district, just steps from the Jardin du Ranelagh. Located in an ultra-high-end Haussmann-style building featuring a resident concierge (7 days a week) and a classic Parisian elevator. An exceptional 550 m² apartment, designed and styled by a renowned Parisian architect. Situated on the *étage noble* (principal floor) and featuring a continuous balcony, the layout includes: an elegant contemporary reception gallery, a triple living area comprising a lounge, dining room, and bar, plus a semi-open kitchen worthy of a Michelin-starred chef. It offers 5 bedroomsincluding a royal suite with an oversized walk-in closetalong with five private bathrooms and multiple restrooms. Additionally, a home cinema, a poker room, and secure parking complete this exceptional property. High-end, state-of-the-art amenities include a home automation system and air conditioning; the building benefits from 24/7 security. A rare find on the market. View immediately (medium-term rentals accepted). - Scheduled for delivery in October 2026.

This spectacular flat for rent, located on the penthouse, 12th floor north of Madrid, offers a unique living experience. Surrounded by an extensive perimeter terrace, it allows you to enjoy incredible views. The property, loft-style, has one bedroom and a modern bathroom, open kitchen, and a splendid and spacious living room surrounded by windows with wonderful panoramic views. The interior guarantees comfort and elegance. Its spacious and well-lit areas create a welcoming atmosphere to fully enjoy the home. The flexibility of the open space allows for changes and adaptations, with the possibility of creating more rooms, bedrooms, and even a new bathroom. Located in the modern northern area of Madrid, the property offers proximity to all kinds of services, restaurants, leisure areas, a prestigious shopping center, universities, making it the ideal option for those seeking comfort and convenience in the heart of the city.

PERIOD CHARM AND REMARKABLE VOLUMES CATHERINE PIGUET is pleased to present this superb six-room family and reception apartment, located on the piano nobile of an elegant freestone mansion built in the early 20th century. Offering exceptional proportions and a perfectly balanced layout, the property harmoniously combines grand reception areas with comfortable family living spaces. Boasting an impressive ceiling height of 3.80 metres (12.5 feet), this distinguished residence has preserved all the hallmarks of classic Parisian architecture, including original parquet flooring, exquisite moldings, and period fireplaces, lending the property timeless elegance and authentic character.Dual-aspect and flooded with natural light, the apartment benefits from an East-West exposure, ensuring sunshine throughout the day. Its open views, free from overlooking neighbours, further enhance the sense of space, brightness, and tranquillity that defines this exceptional property. CHARME DE L’ANCIEN ET VOLUMES REMARQUABLES CATHERINE PIGUET vous propose, au sein de l’étage noble d’un élégant hôtel particulier en pierre de taille édifié au début du XXème siècle, un superbe appartement de réception et de famille de 6 pièces, bénéficiant de volumes rares et d’une distribution particulièrement harmonieuse. Doté d’une exceptionnelle hauteur sous plafond de 3,80 mètres, ce bien d’exception a su préserver l’intégralité des attributs de l’architecture classique parisienne : parquets d’origine, moulures raffinées et cheminées d’époque, conférant à l’ensemble un cachet authentique et intemporel. Traversant et baigné de lumière naturelle, l’appartement profite d’une double exposition Est/Ouest qui lui assure un ensoleillement optimal tout au long de la journée. Les vues dégagées, sans aucun vis-à-vis, renforcent la sensation d’espace et de sérénité qui se dégage de ce lieu rare.

Set in the prestigious Rond Point des Pistes neighbourhood, these ski-in ski-out Méribel apartments not only have the vast Three Valleys on the doorstep but also a good selection of restaurants, shops and bars. From here, you can easily walk or ski down to the centre of Méribel where you can find even more services. About the Location Part of the world’s largest ski area, the Three Valleys, sporty Méribel is a world-class resort with access to 600km of interconnected slopes and a further 120km of cross country skiing. This means that no two days are the same. Impressive skiing credentials aside, Méribel is well-loved for its pretty chalet-style architecture, welcoming village atmosphere and sunny aspect. During the warmer months, Méribel turns into a summer sports paradise. With ribbons of trails waiting to be explored, on foot or by bicycle, and an 18-hole golf course with breathtaking views, there is something for the whole family to enjoy. The resort comprises several different villages, each with its own ambience and charm. This brand-new collection of apartments and penthouses occupies an unrivalled ski-in ski-out spot in the coveted Rond Point des Pistes neighbourhood, one of the highest and sunniest parts of Méribel. About the Property Created by a local developer who has years of experience in Méribel and an excellent track record, Alba will be built in a traditional style with a sloping roof and a facade made from wood and stone. Spanning 157 sqm, this 3 bedroom apartment will be set on the first floor of the residence with a terrace for enjoying the late evening sun and taking in the wonderful views over the valley. Inside, the apartment will feature an open-plan living and dining area with oak parquet flooring and brushed spruce wood panelling on the walls to give it a welcoming, Alpine ambience. The future owners will also have the option to choose their preferred finishes from a curated selection of styles, allowing them to make their mark on the property. The apartment also comes with a bunk bedroom, ideal for accommodating young children and providing flexible sleeping space for guests. Investment Potential Without a doubt, le Rond des Pistes is the most premium part of Méribel with prices ranging going up to €40,000 per sqm. The high-end finishes, exceptional location and large outdoor areas of this project are unbeatable. Recent investment has been poured into the area with old hotels being turned into apartments, which means that it has been fully renovated creating a charming new neighbourhood. If future owners decide to rent their property out, they may be able to reclaim the VAT on the property price. ATHENA ADVISERS - Added value and 360° purchase support since 2003 In addition to organising property viewings from our offices in the French Alps and Cannes, our in-house teams also support clients through every step of the purchase process: accessing the 20% VAT rebate programme, finding the best French mortgage at a low rate, and introducing you to the best rental management company via our in-house service or partner agencies. We also decode the paperwork and contracts and become the bridge between all the different legal and official parties involved in the purchase, guiding our clients through every step of the process.

Available for long-term rental, this elegant 100 sqm apartment offers an exceptional lifestyle just minutes from the centre of Cannes. Located on the 8th and top floor, the property enjoys a south-facing exposure and opens onto a 15 sqm terrace boasting breathtaking panoramic views over the Mediterranean Sea, the Bay of Cannes, the Lérins Islands and the iconic Croix des Gardes monument. The apartment features an inviting entrance hall, a spacious and light-filled living and dining area, a separate fully equipped kitchen, two generously sized bedrooms, each with its own en-suite bathroom and WC, ensuring both comfort and privacy. Residents benefit from premium amenities including a beautifully landscaped park, a swimming pool and tennis courts, all within a secure and peaceful environment. A private garage and cellar complete this exceptional property, perfectly suited for those seeking an exclusive long-term residence on the French Riviera.

Located in the sought-after La Californie district of Cannes, in the heart of a vast private park with a swimming pool and tennis courts. Luxurious, secure residence with a concierge service. Situated on a high floor, this 97 sqm, 3-room apartment features a 25 sqm terrace offering exceptional panoramic sea views over the Bay of Cannes, the Esterel mountains, Palm Beach and the Lérins Islands. The apartment comprises a bright living room, a fully equipped kitchen, two bedrooms and two bathrooms. Cellar and underground garage included.

Apartment at Aura Towers Immediate availability. A 78 m² furnished apartment located on the 3rd floor of the Aura Towers development—ideal for executives or young couples seeking comfort, a prime location, and modern design. Upon entering, you are greeted by an open-concept kitchen integrated with the living and dining areas, creating a functional and inviting space for entertaining guests or working from home. It features two bedrooms: the master suite includes a walk-in closet and private bathroom, while the second bedroom serves perfectly as a home office or guest room. Additionally, the unit includes a second full bathroom and two parking spaces. The apartment comes fully furnished (living room, dining area, bedrooms with beds, basic appliances, and decorative touches), boasting contemporary finishes and abundant natural light. From the building's common areas, residents can enjoy panoramic views of the city and the "Pirámide del Pueblito." Building amenities include a gym, swimming pool, BBQ area, laundry facilities, and 24/7 security. Strategically located in Corregidora along the *Libramiento Sur Poniente* (Southwest Bypass), the property offers easy access to services, major roadways, and shopping centers. Move-in ready: practical, cozy, and low-maintenance—perfect for those seeking a blend of style and functionality. Property represented by Angie Garduño of Querétaro Sotheby’s International Realty. AI has been used in some of the photos; therefore, some images are for illustrative purposes.

REF 3796 - Collective heating and hot water - Located just 150m from the Porte d'Ivry Metro station (line 7) and at the foot of a Vélib' station, on the 4th floor of a recent residence from 2005, a 113 m² loft-style apartment with a 20 m² green terrace offering a panoramic view of Paris. The apartment includes an entrance, a spacious living room opening onto the terrace, a fitted and equipped kitchen, as well as two bedrooms each with their own adjoining bathroom: one with a shower room and wardrobes, the other with a bathroom and a wardrobe. An independent toilet completes the package. A particularly pleasant living environment. Shops and amenities are immediately nearby. Parking space in the basement (an additional 100€). Cosy Home comfort rating 4 sofa.This description has been automatically translated from French.

Rue du centre - On the sixth and top floor of a modern building, magnificent furnished apartment of 208.17 m² (2,240 sq ft), enjoying breathtaking views over La Défense and Paris from its exceptional roof terrace. The apartment opens onto an entrance hall with cloakroom and technical space, leading to a spacious living/dining room extended by a fitted kitchen, with direct access to a long balcony. The sleeping quarters comprise a master suite with balcony and private shower room, two additional bedrooms — one with balcony — a bathroom, a laundry room, extensive storage space, and a separate toilet. Upstairs, a striking feature: a glazed dining room with kitchen, opening onto a 360° landscaped terrace offering unobstructed, uninterrupted views. Air conditioning, roof terrace, unobstructed views, collective gas heating and hot water. A cellar and one parking space complete this exceptional property. Availability: immediate Rent: €12,900.00/month, charges included Security deposit: €25,280.00 (two months' base rent) Fees for Primary residence lease (Loi Alur): €12.10 / m² incl. VAT + €3.03 / m² incl. VAT for the check-in inspection, i.e.: €3,149.61 incl. VAT Fees for Secondary residence or corporate lease (Code Civil): 10% of annual rent excluding charges + VAT (20%), i.e.: €18,201.60 incl. VAT (including €3.03 / m² incl. VAT for the check-in inspection, i.e. €630.75 incl. VAT) Montant estimé des dépenses annuelles d'énergie pour un usage standard, établi à partir des prix de l'énergie de l'année 2024 : 2070€ ~ 2810€ - Les informations sur les risques auxquels ce bien est exposé sont disponibles sur le site Géorisques : www.georisques.gouv.fr

AVAILABLE NOW FOR 10-12 MONTHS Elegant two-bedroom luxury apartment with sea views on La Croisette, steps from the Palais des Festivals. Newly renovated and beautifully appointed, this high-end apartment is located on the first floor of a renowned historic building on La Croisette. Just a short stroll from the Palais des Festivals, it offers an exceptional combination of prestige, comfort, and convenience. Set in one of Cannes' most sought-after positions, the residence benefits from a main entrance opening directly onto La Croisette, placing beaches, luxury boutiques, and fine dining just moments away. The apartment features refined designer furnishings throughout and a bright, modern living space with a large TV and a fully equipped contemporary kitchen. It comprises two spacious bedrooms, each fitted with 180 cm beds and its own en-suite bathroom, ensuring both comfort and privacy. A charming balcony offers pleasant views over La Croisette and the Mediterranean Sea, providing an ideal spot to relax. A well equipped fitness room and indoor pool are both available to guests. Situated on the first floor of a prestigious historic Cannes building, the apartment benefits from elevator access. Furnished rental Lease : Secondary residence Monthly rent: 11,500€/ month from Sept to June or 15,000€/ month for a 12 months lease Security deposit: 2 months’ rent Utilities (water, electricity, internet): payable by the tenant Tenant fees: 1 month’s rent + VAT Full advance payment or 3 months advance payment + GarantMe insurance required.

High above Zurich, on the 23rd floor of the Mobimo Tower, this luxurious penthouse offers breathtaking views of the city, Lake Zurich, and the Alps. With premium materials, exclusive amenities, and access to the five-star services of the Renaissance hotel, this living experience is truly one of a kind. You can find more detailed information about this property on our website.

An exclusive 284 m² penthouse located in a prime position adjacent to Cuburski Park, just a short walk from the Saint Sava Temple. This exceptional residence is defined by its spacious layout, abundant natural light, and complete privacy. The apartment features five rooms, five bathrooms, and a fully equipped kitchen, offering outstanding comfort and functionality. It also boasts a spacious corner terrace extending along two sides of the apartment, as well as an impressive rooftop terrace with breathtaking panoramic views of the entire city and direct views of Cuburski Park. The rooftop terrace is the property's standout feature, providing the perfect setting for private events, entertaining guests, or simply enjoying complete privacy, tranquility, and spectacular views. The property includes three parking spaces, adding further convenience and exclusivity. This penthouse represents a rare opportunity to acquire a luxury residence in one of Vracar's most prestigious locations, combining an exceptional setting, expansive outdoor terraces, privacy, and remarkable city views.

Exclusively, Real Estate Passion - Paris, suggests: In one of the capital's most beautiful addresses on Île Saint Louis, facing the Seine. In a freestone building designed by a renowned architect. An exceptional 450 sq m apartment with a 24/7 concierge and a Parisian elevator. On the second floor, the apartment boasts an exceptional view with a full-length balcony overlooking the Seine and the Eiffel Tower. It offers the following amenities: It features two reception galleries, a vestibule, a triple living room with a breathtaking view of the Seine of over 100 sq m, a formal dining room that can accommodate 10 to 12 guests, a bar, and two separate kitchens designed by a Michelin-starred chef. Featuring four suites, including a royal suite, each with a dressing room and two private bathrooms, two private powder rooms, and several toilets throughout the apartment. High-end high-tech amenities, home automation system. Parking included in a secure building with a 7/7 concierge. A truly privileged setting, protected from prying eyes. Please consult (short-term rentals accepted). ***In addition, a high-end service, including champagne, a bouquet of flowers, welcome products, toiletries, luxury bedding, tableware, entry/exit cleaning and a 7/7 concierge service, is included during your stay.***

Welcome to Marina Blue where luxury living meets urban convenience in the heart of Miami! This stunning one-bedroom residence offers breathtaking views, and a central location. Enjoy an open floor plan, floor-to-ceilingwindows, and a sleek kitchen. Amenities include 2 pools, fitness center, volleyball court, 24-hour security andmore! Located in Downtown Miami, you'll have easy access to the arena, nightlife, shopping, and dining. Don'tmiss out on this opportunity to experience the epitome of Miami living!

Enjoy this 1 BR/2BA southwest corner model with spectacular ocean and coastline views at highly desirable Point of Americas I. The second bedroom has been converted to living space and now features an oversized living and dining area, new and updated baths, new A/C, new appliances, wraparound balcony and more. Partially furnished. Five star resort amenities including grand lobby, restaurant, fitness center, guest rooms, lush pools and beach attendant service on the widest private beach in Fort Lauderdale. Just minutes to Las Olas & downtown, airport, Brightline and all major roads. Annual unfurnished lease only and includes cable and Internet as provided by the condominium association.

Real Estate Passion - Paris suggest, In one of the capital's most prestigious addresses, on the renowned Rue Bassano, in the heart of Paris's Golden Triangle. Located in a very secure, high-end Haussmannian building with 24/7 concierge service and a Parisian elevator. This luxurious 238 sq m duplex, spread over two levels, was designed and signed by a famous Parisian architect. On the fifth and sixth floors, boasting exceptional views of the Eiffel Tower and Sacré-Cœur Basilica from a continuous balcony, it offers the following amenities: a delightful contemporary reception gallery connected by a wrought-iron staircase, a vestibule, a triple living room with a formal dining room, a bar, and a semi-open kitchen designed by a Michelin-starred chef. Featuring three bedrooms, including a majestic suite in a rotunda with an expansive walk-in closet, a bathroom, two private shower rooms, and several toilets throughout the apartment. High-end, high-tech amenities and air conditioning. Secure building with 24/7 concierge service. A master office and a parking space complete this exceptional duplex. A rare find on the market, available for immediate viewing. (Long, Short and medium-term rentals accepted). ***In addition, a high-end service, including champagne, a bouquet of flowers, welcome products, toiletries, luxury bedding, tableware, entry/exit cleaning and a 7/7 concierge service, is included during your stay.***

Exquisite one-bedroom, one-bathroom fully furnished residence at Icon Brickell, offering an unparalleled living experience. Residents can indulge in world-class five-star amenities, savor exceptional dining at on-site restaurants, and enjoy a host of premium features designed for comfort and luxury.

Located on the 13th floor of Torres del Parque, this spacious apartment offers an exceptional combination of generous living areas, abundant natural light, and breathtaking views of La Sabana Metropolitan Park. With approximately 230 m² (2,476 sq. ft.) of living space, the residence features three bedrooms, three full bathrooms, a semi-equipped kitchen, expansive living and dining areas, two private parking spaces, and four private balconies overlooking La Sabana and the iconic National Stadium. Designed for both comfort and functionality, the apartment boasts bright, airy interiors and excellent cross ventilation, creating a welcoming atmosphere ideal for families, executives, or anyone seeking an elevated urban lifestyle. Residents of Torres del Parque enjoy a variety of amenities, including: Social event room 24/7 security Family-friendly environment One of the property's greatest advantages is its prime location, directly across from La Sabana Metropolitan Park and just minutes from major corporate offices, free trade zones, prestigious universities, shopping centers, supermarkets, restaurants, and leading medical facilities. With easy access to downtown San José, Heredia, Alajuela, and Juan Santamaría International Airport—approximately 20 minutes away—the residence offers outstanding connectivity to Costa Rica's most important destinations. This apartment presents an exceptional opportunity to enjoy spacious living, spectacular park views, and one of San José's most sought-after residential locations.

BARNES Madrid is renting this exclusive, renovated, and furnished 130 m² apartment in the Centro district, in the Universidad neighborhood. It is located in a classic building that was completely renovated in 2022 by the renowned firm Rafael Robledo Arquitectos. It combines the essence of Madrid’s architecture with the highest standards in design, technology, and comfort, featuring high-end contemporary interior design. This luxurious property overlooks the iconic Gran Vía and offers unique panoramic views from its large windows and balconies. The building features 24-hour concierge service, a professional gym equipped with state-of-the-art Technogym machines, and an impressive communal rooftop terrace with a solarium and 360° views of the Madrid skyline. Featuring open and bright spaces, it includes a spacious living-dining room with floor-to-ceiling windows, two exterior double bedrooms with en-suite bathrooms and balconies, a guest restroom, and a semi-open kitchen with custom-paneled cabinetry. The kitchen is fully equipped with high-end appliances, a complete set of kitchenware, and a washer-dryer. Notable comfort features include ducted climate control, underfloor heating and cooling with independent thermostats, mechanical ventilation and exhaust systems, as well as a smart lighting system that allows for efficient control of lighting settings and energy consumption. Utility costs can be included for an additional fee. There is the option to rent up to two parking spaces and