Definition:Uniformizable Space

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Then $T$ is uniformizable if and only if there exists a uniformity $\UU$ on $S$ such that $\struct {\struct {S, \UU}, \tau}$ is a uniform space.

Also see

• Definition:Quasiuniformizable Space

• $T_{3 \frac 1 2}$ Space is Uniformizable

Linguistic Note

The British English spelling for uniformizable is uniformisable.

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