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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Closed sets which are not $CS^{\infty}$-critical


Author: Cornel Pintea
Journal: Proc. Amer. Math. Soc. 133 (2005), 923-930
MSC (2000): Primary 55R05; Secondary 55Q05, 55N10
Published electronically: 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 $n$-dimensional manifold $M$has large $(n-1)$-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 $M$, are not critical sets for some special real or $S^1$-valued functions.


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Additional Information

Cornel Pintea
Affiliation: Babeş-Bolyai University, Faculty of Mathematics and Computer Sciences, 400084 M. Kogalniceanu 1, Cluj-Napoca, Romania
Email: cpintea@math.ubbcluj.ro

DOI: http://dx.doi.org/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
Published electronically: September 16, 2004
Additional Notes: This research was partially supported by the European Research and Training Network Geometric Analysis, Contract Number: HPRN-CT-1999-00118
Communicated by: Paul Goerss
Article copyright: © Copyright 2004 American Mathematical Society