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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On extending homeomorphisms to Fréchet manifolds


Authors: R. D. Anderson and John D. McCharen
Journal: Proc. Amer. Math. Soc. 25 (1970), 283-289
MSC: Primary 57.55
MathSciNet review: 0258064
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0258064-5
PII: S 0002-9939(1970)0258064-5
Keywords: Fréchet manifolds, infinite-dimensional manifolds, $ Z$-sets, Property $ Z$, homeomorphism extension, ambient isotopy
Article copyright: © Copyright 1970 American Mathematical Society