A characterization of uniform paracompactness

Fried, J.; Frolík, Z.

doi:10.1090/S0002-9939-1983-0715882-3

A characterization of uniform paracompactness
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by J. Fried and Z. Frolík PDF

Proc. Amer. Math. Soc. 89 (1983), 537-540 Request permission

Abstract:

Main result: a uniform space $X$ is uniformly paracompact [R] iff for some (and then any) compactification $K$ of $X$ and for any compact $C \subset K\backslash X$ closed disjoint sets $X \times C$ and the diagonal ${\Delta _X}( = \{ \left \langle {x,x} \right \rangle |x \in X\} )$ can be separated by a uniformly continuous function on the semiuniform product $X * K$.

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