continuous space

Analogously to a smooth space, a **continuous space** is any notion of space between which the morphisms are continuous maps. Examples include:

Contrast this with, for example:

- uniform spaces (morphisms are uniformly continuous maps),
- smooth spaces (morphisms are smooth maps),
- (weak) homotopy types (objects are still (nice) topological spaces, but now morphisms are homotopy classes of continuous maps).