Closed sets which are not $CS^{\infty }$-critical
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- by Cornel Pintea PDF
- Proc. Amer. Math. Soc. 133 (2005), 923-930 Request permission
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.References
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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
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 923-930
- MSC (2000): Primary 55R05; Secondary 55Q05, 55N10
- DOI: https://doi.org/10.1090/S0002-9939-04-07584-7
- MathSciNet review: 2113945