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A result about a selection problem of Michael


Authors: Francis Jordan and Sam B. Nadler Jr.
Journal: Proc. Amer. Math. Soc. 129 (2001), 1219-1228
MSC (1991): Primary 54C65, 54E40; Secondary 54F15
DOI: https://doi.org/10.1090/S0002-9939-00-05598-2
Published electronically: September 25, 2000
MathSciNet review: 1707150
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Abstract:

It is shown that a continuum that is an $S_4$ space in the sense of Michael must be hereditarily decomposable. This improves known results, thereby providing more evidence that such continua must be dendrites.


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Additional Information

Francis Jordan
Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292-0001

Sam B. Nadler Jr.
Affiliation: Department of Mathematics, West Virginia University, Morgantown, West Virginia 26506-6310

DOI: https://doi.org/10.1090/S0002-9939-00-05598-2
Keywords: Connectivity functions, continuous selections, $\mathfrak c$-connected, hereditarily decomposable continua, indecomposable continua, $S_4$ spaces
Received by editor(s): July 9, 1998
Received by editor(s) in revised form: June 15, 1999
Published electronically: September 25, 2000
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society