Is There a Curvature in Space?

Gravity is not like a force the way we think about other forces, but instead, it's a fictitious force. It's a force that appears to act because we can't see that space is curved. If you're building a universe, and i'm giving you pieces of it, ria each piece has curvature. So if i only give you curved pieces, what kind of big universe shape can you build? When you can't build like an infinitely flat space, like a huge sheet, but you could build like a sphere, or a circle, or a doughnut, or something else that has a curved surface.