Docility at infinity and compactifications of ANR’s

Sher, R. B.

doi:10.1090/S0002-9947-1976-0425925-3

Docility at infinity and compactifications of ANR’s
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by R. B. Sher PDF

Trans. Amer. Math. Soc. 221 (1976), 213-224 Request permission

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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