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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Stationary isotopies of infinite-dimensional spaces

Author: Raymond Y. T. Wong
Journal: Trans. Amer. Math. Soc. 156 (1971), 131-136
MSC: Primary 57.55; Secondary 54.00
MathSciNet review: 0275476
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Abstract: Let X denote the Hilbert cube or any separable infinite-dimensional Fréchet space. It has been shown that any two homeomorphisms f, g of X onto itself is isotopic to each other by means of an invertible-isotopy on X. In this paper we generalize the above results to the extent that if f, g are K-coincident on X (that is, $ f(x) = g(x)$ for $ x \in K$), then the isotopy can be chosen to be K-stationary provided K is compact and has property-Z in X. The main tool of this paper is the Stable Homeomorphism Extension Theorem which generalizes results of Klee and Anderson.

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Keywords: Invertible-isotopy, K-coincident, K-stationary, homeomorphism, property-Z, stable homeomorphism extension
Article copyright: © Copyright 1971 American Mathematical Society