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
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 $3.1.5$
