Annulus conjecture and stability of homeomorphisms in infinite-dimensional normed linear spaces

McCoy, R. A.

doi:10.1090/S0002-9939-1970-0256419-6

Annulus conjecture and stability of homeomorphisms in infinite-dimensional normed linear spaces
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by R. A. McCoy

Proc. Amer. Math. Soc. 24 (1970), 272-277

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

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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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