Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54F15, 54F35, 54F65

Retrieve articles in all journals with MSC: 54F15, 54F35, 54F65


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1246530-2
PII: S 0002-9939(1995)1246530-2
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