Annulus conjecture and stability of homeomorphisms in infinite-dimensional normed linear spaces
Author:
R. A. McCoy
Journal:
Proc. Amer. Math. Soc. 24 (1970), 272-277
MSC:
Primary 57.55; Secondary 54.00
DOI:
https://doi.org/10.1090/S0002-9939-1970-0256419-6
MathSciNet review:
0256419
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Abstract | References | Similar Articles | Additional Information
Abstract: If $E$ is an arbitrary infinite-dimensional normed linear space, it is shown that if all homeomorphisms of $E$ onto itself are stable, then the annulus conjecture is true for $E$. As a result, this confirms that the annulus conjecture for Hilbert space is true. A partial converse is that for those spaces $E$ which have some hyperplane homeomorphic to $E$, if the annulus conjecture is true for $E$ and if all homeomorphisms of $E$ onto itself are isotopic to the identity, then all homeomorphisms of $E$ onto itself are stable.
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Additional Information
Keywords:
Infinite-dimensional normed linear spaces,
Hilbert space,
annulus conjecture,
stable homeomorphisms,
homeomorphisms isotopic to the identity,
engulfing theorem
Article copyright:
© Copyright 1970
American Mathematical Society