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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
MathSciNet review: 0256419
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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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DOI: https://doi.org/10.1090/S0002-9939-1970-0256419-6
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