Homeomorphic Spaces

Definition: Homeomorphic Spaces

Two Topological Spaces $(X,{\tau }_X)$ and $(Y,{\tau }_Y)$ are homeomorphic if there exists a homeomorphism between them.

NOTATION

$(X,{\tau }_X)\cong (Y,{\tau }_Y)$

Theorem

The existence of a homeomorphism is an equivalence relation.

PROOF

TODO