Definition:Homeomorphism/Terminology
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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 $T_\beta$.