Nagata-Smirnov Metrization Theorem

It has been suggested that this page or section be merged into Smirnov Metrization Theorem. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Mergeto}} from the code.

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

This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Source of Name

This entry was named for Jun-iti Nagata and Yurii Mikhailovich Smirnov.

Sources

• 1975: James R. Munkres: Topology