Definition:Homeomorphism/Topological Spaces

Definition
Let $T_\alpha = \struct {S_\alpha, \tau_\alpha}$ and $T_\beta = \struct {S_\beta, \tau_\beta}$ be topological spaces.

Let $f: T_\alpha \to T_\beta$ be a bijection.

Also known as
Also known as:
 * a topological equivalence, usually used when the spaces in question are metric spaces
 * an isomorphism.

Also see

 * Equivalence of Definitions of Homeomorphic Topological Spaces


 * Inverse of Homeomorphism is Homeomorphism