Definition:Topological Equivalence

Homeomorphism: Topological Spaces
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.

Topologically equivalent metrics
Let $M_1 = \struct {A, d_1}$ and $M_2 = \struct {A, d_2}$ be metric spaces on the same underlying set $A$.

Also see

 * Definition:Equivalence