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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Stable homeomorphisms on infinite-dimensional normed linear spaces.


Authors: D. W. Curtis and R. A. McCoy
Journal: Proc. Amer. Math. Soc. 28 (1971), 496-500
MSC: Primary 57.55; Secondary 46.00
MathSciNet review: 0283831
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Abstract: R. Y. T. Wong has recently shown that all homeomorphisms on a connected manifold modeled on infinite-dimensional separable Hilbert space are stable. In this paper we establish the stability of all homeomorphisms on a normed linear space $ E$ such that $ E$ is homeomorphic to the countable infinite product of copies of itself. The relationship between stability of homeomorphisms and a strong annulus conjecture is demonstrated and used to show that stability of all homeomorphisms on a normed linear space $ E$ implies stability of all homeomorphisms on a connected manifold modeled on $ E$, and that in such a manifold collared $ E$-cells are tame.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0283831-2
PII: S 0002-9939(1971)0283831-2
Keywords: Infinite-dimensional normed linear spaces, connected infinite-dimensional manifolds, stable homeomorphisms, collared cells, annulus conjecture
Article copyright: © Copyright 1971 American Mathematical Society