-sets in ANR's

Author:
David W. Henderson

Journal:
Trans. Amer. Math. Soc. **213** (1975), 205-216

MSC:
Primary 54C55; Secondary 57A20

MathSciNet review:
0391008

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Abstract: (1) *Let A be a closed Z-set in an ANR X. Let* *be an open cover of X. Then there is a homotopy inverse* *to the inclusion* *such that f and both homotopies are limited by* .

(2) *If, in addition, X is a manifold modeled on a metrizable locally convex TVS, F, such that F is homeomorphic to* , *then there is a homotopy* *limited by* *such that the closure* (*in X*) *of* *is contained in* .

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1975-0391008-3

Article copyright:
© Copyright 1975
American Mathematical Society