Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$ Z$-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 $ \mathcal{F}$ be an open cover of X. Then there is a homotopy inverse $ f:X \to X - A$ to the inclusion $ X - A \to X$ such that f and both homotopies are limited by $ \mathcal{F}$.

(2) If, in addition, X is a manifold modeled on a metrizable locally convex TVS, F, such that F is homeomorphic to $ {F^\omega }$, then there is a homotopy $ j:X \times I \to X$ limited by $ \mathcal{F}$ such that the closure (in X) of $ j(X \times \{ 1\} )$ is contained in $ X - A$.

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Article copyright: © Copyright 1975 American Mathematical Society