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 | References | Similar Articles | Additional Information

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 such that 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 implies stability of all homeomorphisms on a connected manifold modeled on , and that in such a manifold collared -cells are tame.

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DOI:
https://doi.org/10.1090/S0002-9939-1971-0283831-2

Keywords:
Infinite-dimensional normed linear spaces,
connected infinite-dimensional manifolds,
stable homeomorphisms,
collared cells,
annulus conjecture

Article copyright:
© Copyright 1971
American Mathematical Society