Definition:Topologically Equivalent Metrics

Definition
Let $A$ be a set upon which there are two metrics imposed: $d_1$ and $d_2$.

Then $d_1$ and $d_2$ are topologically equivalent iff:


 * $U \subseteq A$ is $d_1$-open $\iff$ $U \subseteq A$ is $d_2$-open.

Also see

 * Metric Spaces are Topologically Equivalent iff Continuity Preserved


 * Homeomorphism