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

 

Docility at infinity and compactifications of ANR's


Author: R. B. Sher
Journal: Trans. Amer. Math. Soc. 221 (1976), 213-224
MSC: Primary 54F40; Secondary 54C55
MathSciNet review: 0425925
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Abstract: Various conditions of contractibility and extensibility at $ \infty $ for locally compact metric spaces are studied. These are shown to be equivalent if the space under consideration is an absolute neighborhood retract (ANR) and an ANR satisfying them is called docile at $ \infty $. Docility at $ \infty $ is invariant under proper homotopy domination. The ANR X is docile at $ \infty $ if and only if FX (the Freudenthal compactification of X) is an ANR and $ FX - X$ is unstable in FX; the inclusion of X into FX is a homotopy equivalence.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0425925-3
PII: S 0002-9947(1976)0425925-3
Keywords: Absolute proper retract, docility at $ \infty $, Freudenthal compactification, proper homotopy domination, unstable sets
Article copyright: © Copyright 1976 American Mathematical Society