Metrizable iff Regular and has Sigma-Locally Finite Basis
Jump to navigation
Jump to search
This theorem requires a proof..
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
 It has been suggested that this page or section be merged into Nagata-Smirnov Metrization Theorem. (Discuss) |
Theorem
Let $T = \struct {S, \tau}$ be a topological space.
Then $T$ is metrizable if and only if $T$ is regular and has a $\sigma$-locally finite basis.
Proof
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
When this page/section has been completed, {{ProofWanted}} should be removed from the code.
If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page (see the proofread template for usage).
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: Metrizability
