Stable homeomorphisms on infinite-dimensional normed linear spaces.
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- by D. W. Curtis and R. A. McCoy
- Proc. Amer. Math. Soc. 28 (1971), 496-500
- DOI: https://doi.org/10.1090/S0002-9939-1971-0283831-2
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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.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 28 (1971), 496-500
- MSC: Primary 57.55; Secondary 46.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0283831-2
- MathSciNet review: 0283831