Definition:Uniform Space
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Definition
Let $\UU$ be a uniformity on a set $S$.
The quasiuniform space $\struct {\struct {S, \UU}, \tau}$ generated from $\UU$ is a uniform space.
Also see
- Quasiuniformity Induces Topology for a proof that $\tau$ is actually a topology.
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
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): uniform space