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A generalization of Kelley's theorem for $C$-spaces

Author(s): Michael Levin; James T. Rogers Jr.
Journal: Proc. Amer. Math. Soc. 128 (2000), 1537-1541.
MSC (1991): Primary 54F45, 54F15
Posted: October 5, 1999
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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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Additional Information:

Michael Levin
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118-5698
Email: levin@mozart.math.tulane.edu

James T. Rogers Jr.
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118-5698
Email: jim@math.tulane.edu

DOI: 10.1090/S0002-9939-99-05158-8
PII: S 0002-9939(99)05158-8
Keywords: $C$-spaces, continua, dimension
Received by editor(s): March 31, 1998
Received by editor(s) in revised form: July 1, 1998
Posted: October 5, 1999
Communicated by: Alan Dow
Copyright of article: Copyright 2000, American Mathematical Society

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