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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Menger manifolds homeomorphic to their $ n$-homotopy kernels

Author: Yutaka Iwamoto
Journal: Proc. Amer. Math. Soc. 123 (1995), 945-953
MSC: Primary 54F15; Secondary 54F35, 54F65
MathSciNet review: 1246530
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Abstract: We give a necessary and sufficient condition that an $ (n + 1)$-dimensional Menger manifold ( $ {\mu ^{n + 1}}$-manifold) is homeomorphic to its n-homotopy kernel. Such a $ {\mu ^{n + 1}}$-manifold is called a $ \mu _\infty ^{n + 1}$-manifold. We also prove the following results:

(1) Each homeomorphism between two Z-sets in a $ \mu _\infty ^{n + 1}$-manifold M extends to an ambient homeomorphism of M onto itself if it is n-homotopic to id in M.

(2) An n-homotopy equivalence between two $ \mu _\infty ^{n + 1}$-manifolds is n-homotopic to a homeomorphism.

(3) Each map from a $ \mu _\infty ^{n + 1}$-manifold into a $ {\mu ^{n + 1}}$-manifold is n-homotopic to an open embedding.

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Keywords: Menger manifold, n-homotopy, n-homotopy kernel, properly n-contractible to $ \infty $, properly locally n-contractible at $ \infty$, $ u_\infty ^{n + 1}$-manifold, [0, 1)-stable Q-manifold
Article copyright: © Copyright 1995 American Mathematical Society

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