A generalization of Kelley’s theorem for 𝐶-spaces

Levin, Michael; Rogers, James, Jr.

doi:10.1090/S0002-9939-99-05158-8

A generalization of Kelley’s theorem for $C$-spaces
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by Michael Levin and James T. Rogers Jr. PDF

Proc. Amer. Math. Soc. 128 (2000), 1537-1541 Request permission

Abstract:

We prove that if an open map $f:X \longrightarrow Y$ of compacta $X$ and $Y$ has perfect fibers and $Y$ is a $C$-space, then there exists a $0$-dimensional compact subset of $X$ intersecting each fiber of $f$. This is a stronger version of a well-known theorem of Kelley. Applications of this result and related topics are discussed.

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