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Closed sets which are not  -critical
Author(s):
Cornel
Pintea
Journal:
Proc. Amer. Math. Soc.
133
(2005),
923-930.
MSC (2000):
Primary 55R05;
Secondary 55Q05, 55N10
Posted:
September 16, 2004
MathSciNet review:
2113945
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Abstract:
In this paper we first observe that the complement of a countable closed subset of an  -dimensional manifold  has large  -homology group. In the last section we use this information to prove that, under some topological conditions on the given manifold, certain families of fibers, in the total space of a fibration over  , are not critical sets for some special real or  -valued functions.
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Additional Information:
Cornel
Pintea
Affiliation:
Babes-Bolyai University, Faculty of Mathematics and Computer Sciences, 400084 M. Kogalniceanu 1, Cluj-Napoca, Romania
Email:
cpintea@math.ubbcluj.ro
DOI:
10.1090/S0002-9939-04-07584-7
PII:
S 0002-9939(04)07584-7
Keywords:
Closed countable sets,
homology and homotopy groups of fiber spaces,
critical points.
Received by editor(s):
November 12, 2002
Received by editor(s) in revised form:
November 9, 2003
Posted:
September 16, 2004
Additional Notes:
This research was partially supported by the European Research and Training Network \textit{Geometric Analysis}, Contract Number: HPRN-CT-1999-00118
Communicated by:
Paul Goerss
Copyright of article:
Copyright
2004,
American Mathematical Society
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