Definition:Topology Induced by Metric

Definition
Let $M = \left({A, d}\right)$ be a metric space.

Also see

 * Equivalence of Definitions of Topology Induced by Metric


 * Metric Induces Topology, in which it is shown that $\tau$ is, in fact, a topology on $M$
 * Subspace Topology (sometimes also called the induced topology)