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

DOI:
https://doi.org/10.1090/S0002-9947-1971-0275476-X

MathSciNet review:
0275476

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Abstract | References | Similar Articles | Additional Information

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, for ), 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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1971-0275476-X

Keywords:
Invertible-isotopy,
*K*-coincident,
*K*-stationary,
homeomorphism,
property-Z,
stable homeomorphism extension

Article copyright:
© Copyright 1971
American Mathematical Society