Since homeomorphisms are excellent equivalence relations in topology , spaces can be distinguished using topological invariants: in order to prove that two topological spaces are not homeomorphic, it is sufficient to find a topological invariant that is different for both spaces. For example, spaces with a different number of open sets are topologically different.
- Number of related components
- Isomorphism class of the fundamental group
- Euler characteristic
- Gender of an area
- Betti numbers of a topological space