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On Extending Homeomorphisms to Fréchet Manifolds
R. D. Anderson and John D. McCharen
Proceedings of the American Mathematical Society
Vol. 25, No. 2 (Jun., 1970), pp. 283-289
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2037206
Page Count: 7
You can always find the topics here!Topics: Homeomorphism, Mathematical manifolds, Separable spaces, Topological theorems, Continuous functions, Hilbert spaces, Infinite products, Open intervals, Topology
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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.
Proceedings of the American Mathematical Society © 1970 American Mathematical Society