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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Lefschetz fixed point theorem for noncompact locally connected spaces


Author: R. J. Knill
Journal: Trans. Amer. Math. Soc. 174 (1972), 185-198
MSC: Primary 55C20
MathSciNet review: 0315700
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Abstract: Leray's notion of convexoid space is localized and used to show that if $ f:M \to M$ is a relatively compact map on a locally convex manifold M, and f has no fixed points then its Lefschetz trace is zero. A similar theorem holds for certain adjunction spaces $ Y{ \cup _g}Z$ where Y is Q-simplicial and Z is locally convexoid. A number of other properties of locally convexoid spaces are derived; for example, any neighborhood retract of a locally convexoid space is locally convexoid.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0315700-9
PII: S 0002-9947(1972)0315700-9
Keywords: Acyclic carrier, topological vector space, manifold, compact map, Lefschetz trace formula, Q-simplicial space, cone, fixed point
Article copyright: © Copyright 1972 American Mathematical Society