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A result about a selection problem of Michael
Author(s):
Francis
Jordan;
Sam
B.
Nadler Jr.
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1219-1228.
MSC (1991):
Primary 54C65, 54E40;
Secondary 54F15
Posted:
September 25, 2000
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Abstract:
It is shown that a continuum that is an  space in the sense of Michael must be hereditarily decomposable. This improves known results, thereby providing more evidence that such continua must be dendrites.
References:
- 1.
- R. G. Gibson and T. Natkaniec, Darboux-like functions, Real Anal. Exchange 22(2) (1996-97), 492-533. MR 98h:26004
- 2.
- M. Hagan, Equivalence of connectivity maps and peripherally continuous transformations, Proc. Amer. Math. Soc. 17 (1966), 175-177. MR 33:3268
- 3.
- O. H. Hamilton, Fixed points for certain noncontinuous transformations, Proc. Amer. Math. Soc. 8 (1957), 750-756. MR 19:301b
- 4.
- J. Jastrzebski, J. Jedrzejewski, and T. Natkaniec, On some subclasses of Darboux functions, Fund. Math. 138 (1991), 165-173. MR 92h:26006
- 5.
- K. Kuratowski, Topology, Vol. 2, Academic Press and Polish Scientific Publishers, 1968. MR 41:4467
- 6.
- E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71(1951), 152-182. MR 13:54f
- 7.
- S. B. Nadler, Jr., Hyperspaces of sets, Marcel Dekker Inc., New York, Basel 1978. MR 58:18330
- 8.
- S. B. Nadler, Jr., Continuum Theory, Marcel Dekker Inc., New York and Basel and Hong Kong 1992. MR 93m:54002
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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:
10.1090/S0002-9939-00-05598-2
PII:
S 0002-9939(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
Posted:
September 25, 2000
Communicated by:
Alan Dow
Copyright of article:
Copyright
2000,
American Mathematical Society
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