Definition:Topology Induced by Metric/Definition 1

Definition

The topology on the metric space $M = \left({A, d}\right)$ induced by (the metric) $d$ is defined as the set $\tau$ of all open sets of $M$.

Also see

• Equivalence of Definitions of Topology Induced by Metric

Sources

• 1962: Bert Mendelson: Introduction to Topology ... (previous) ... (next): $\S 3.2$: Topological Spaces
• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3.1$: Topological Spaces: Example $3.1.5$