Nagata-Smirnov Metrization Theorem
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 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 basis that is countably locally finite.
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).
Source of Name
This entry was named for Jun-iti Nagata and Yurii Mikhailovich Smirnov.
Sources
- 1975: James R. Munkres: Topology