On extending homeomorphisms to Fréchet manifolds

Anderson, R. D.; McCharen, John D.

doi:10.1090/S0002-9939-1970-0258064-5

On extending homeomorphisms to Fréchet manifolds
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by R. D. Anderson and John D. McCharen

Proc. Amer. Math. Soc. 25 (1970), 283-289

DOI: https://doi.org/10.1090/S0002-9939-1970-0258064-5

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Abstract:

Let $M$ be a Fréchet manifold and $K$ be a $Z$-set in $M$. It is shown that a homeomorphism $h$ of $K$ into $M$ can be isotopically extended to a homeomorphism of $M$ onto $M$ if and only if $h(K)$ is a $Z$-set and $h$ is homotopic to the identity in $M$. Conditions under which the isotopic extension can be required to be “close to” the homotopy are also given.

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