Metrizable iff Regular and has Sigma-Locally Finite Basis
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Theorem
Let $T = \left({S, \tau}\right)$ be a topological space.
Then $T$ is metrizable if and only if $T$ is regular and has a $\sigma$-locally finite basis.
Proof
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Sources
- 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology ... (previous) ... (next): $\text{I}: \ \S 5$: Metrizability
