Definition:Topology Induced by Metric/Definition 2

Definition

The topology on the metric space $M = \struct {A, d}$ induced by (the metric) $d$ is defined as the topology $\tau$ generated by the basis consisting of the set of all open $\epsilon$-balls in $M$.

Also see

• Equivalence of Definitions of Topology Induced by Metric

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $5$: Metric Spaces