## Stationary isotopies of infinite-dimensional spaces

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- by Raymond Y. T. Wong PDF
- Trans. Amer. Math. Soc.
**156**(1971), 131-136 Request permission

## 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.

## References

- R. D. Anderson,
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*Topological properties of the Hilbert cube and the infinite product of open intervals*, Trans. Amer. Math. Soc.**126**(1967), 200–216. MR**205212**, DOI 10.1090/S0002-9947-1967-0205212-3 - R. D. Anderson,
*On topological infinite deficiency*, Michigan Math. J.**14**(1967), 365–383. MR**214041**, DOI 10.1307/mmj/1028999787 - R. D. Anderson,
*Strongly negligible sets in Fréchet manifolds*, Bull. Amer. Math. Soc.**75**(1969), 64–67. MR**238358**, DOI 10.1090/S0002-9904-1969-12146-4
—, - Victor L. Klee Jr.,
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K. Kuratowski, - Raymond Y. T. Wong,
*On homeomorphisms of certain infinite dimensional spaces*, Trans. Amer. Math. Soc.**128**(1967), 148–154. MR**214040**, DOI 10.1090/S0002-9947-1967-0214040-4 - Raymond Y. T. Wong,
*A wild Cantor set in the Hilbert cube*, Pacific J. Math.**24**(1968), 189–193. MR**221487**, DOI 10.2140/pjm.1968.24.189

*Spaces of homeomorphisms of finite graphs*, Illinois J. Math. (to appear).

*Topologie*, vol. 2, 3rd ed., Monografie Mat., Tom 21, PWN, Warsaw, 1961, p. 32 (7). MR

**24**#A2958.

## Additional Information

- © Copyright 1971 American Mathematical Society
- 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