The question of whether space is infinite or finite is a fundamental one in cosmology. Currently, we don't have a conclusive answer. Space may be finite but unbounded, meaning it has a shape like a hypersphere, so if you travel in one direction long enough, you will eventually return to your starting point.
Alternatively, it could be infinite, extending endlessly in all directions. Ongoing research and observations aim to shed light on the geometry and size of the universe, but definitive answers are still elusive.