Definition:Quasiuniformizable Space
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Then $T$ is quasiuniformizable if and only if there exists a quasiuniformity $\UU$ on $S$ such that $\struct {\struct {S, \UU}, \tau}$ is a quasiuniform space.
Also see
- Topological Space is Quasiuniformizable for a demonstration that every topological space is quasiuniformizable.
Linguistic Note
The British English spelling for quasiuniformizable is quasiuniformisable.
It would be convenient if there could be a simpler term coined which can be used instead. Eight syllables is rather a lot. On the other hand, as every Topological Space is Quasiuniformizable, the concept is probably not that important to need one.
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