Jerry's Digital Garden

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/Part 2: General Topology/Chapter 6: Uniform Spaces/Section 6.4: Compact Uniform Spaces

Proposition 6.4.6.label Let $X$ be a compact Hausdorff space, then there exists a unique uniformity on $X$ that induces its topology.

Proof. By Proposition 5.24.5, there exists a uniformity on $X$ that induces its topology. By Proposition 6.4.5, $X$ admits a unique uniformity.$\square$

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Jerry's Digital Garden

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