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Definition

Given a metric space $(X,d)$, the metric topology on $X$ is the structure of a topological space on $X$ which is generated from the basis of a topology? given by the open balls

$B(x,r) \coloneqq \{y \in X \;|\; d(x,y) \lt r \}$

for all $x \in X$ and $r \in (0,\infty) \subset \mathbb{R}$.

A topological space whose topology is the metric topology for some metric space structure on its underlying set is called a metrizable topological space.

Last revised on January 7, 2018 at 01:52:50. See the history of this page for a list of all contributions to it.