T3 1/2 Space is Uniformizable

Theorem

Let $T$ be a topological space.


Then $T$ is uniformizable if and only if $T$ is a $T_{3 \frac 1 2}$ space.


Proof


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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: Uniformities
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