Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54F40, 54C55

Retrieve articles in all journals with MSC: 54F40, 54C55

Additional Information

Keywords: Absolute proper retract, docility at $ \infty $, Freudenthal compactification, proper homotopy domination, unstable sets
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society