# Contents

## 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

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

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.

Revised on June 21, 2017 04:25:17 by Urs Schreiber (131.220.184.222)