When you use it as an amount of an area in general, then it's uncountable so you use the singular form. For instance: "travelling to space" or "I need space for my new wardrobe". But if you mean the area for specific purpose & you can actually count it, then you use the plural form. For example: "parking spaces" or "spaces between books on the shelf". In your example, as far as I can see, "spaces" basically mean rooms, so you can use the plural, it won't be a mistake.