<-- Go Back Last Updated: 11/01/2025

Metric Topology**

Given a metric space \((X,d)\), the metric topology \(\mathcal{T}_d\) on \(X\) has as its open sets precisely those sets \(U\) such that every point of \(U\) is contained in an open ball contained in \(U\), i.e. \(\mathcal{T}_d:=\{U\subseteq X|\forall x\in U:\exists r_x>0:B_{r_x}(x)\subseteq U\}\).