Definition:Homeomorphism/Terminology

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

Then $T_\alpha$ and $T_\beta$ are said to be homeomorphic.

The symbolism $T_\alpha \sim T_\beta$ is often seen to denote that $T_\alpha$ is homeomorphic to $T_\beta$.