Stable homeomorphisms on infinitedimensional normed linear spaces.
Authors:
D. W. Curtis and R. A. McCoy
Journal:
Proc. Amer. Math. Soc. 28 (1971), 496500
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 infinitedimensional 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197102838312
PII:
S 00029939(1971)02838312
Keywords:
Infinitedimensional normed linear spaces,
connected infinitedimensional manifolds,
stable homeomorphisms,
collared cells,
annulus conjecture
Article copyright:
© Copyright 1971
American Mathematical Society
