Stationary isotopies of infinitedimensional spaces
Author:
Raymond Y. T. Wong
Journal:
Trans. Amer. Math. Soc. 156 (1971), 131136
MSC:
Primary 57.55; Secondary 54.00
MathSciNet review:
0275476
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Abstract: Let X denote the Hilbert cube or any separable infinitedimensional 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 invertibleisotopy on X. In this paper we generalize the above results to the extent that if f, g are Kcoincident on X (that is, for ), then the isotopy can be chosen to be Kstationary provided K is compact and has propertyZ 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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 , On topological infinite deficiency, Michigan J. Math. 14 (1967), 365383. MR 35 #4893. MR 0214041 (35:4893)
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 , Strongly negligible sets in Fréchet manifolds, Bull. Amer. Math. Soc. 75 (1969), 6467. MR 38 #6634. MR 0238358 (38:6634)
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 , Spaces of homeomorphisms of finite graphs, Illinois J. Math. (to appear).
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 V. L. Klee, Convex bodies and periodic homeomorphisms in Hilbert space, Trans. Amer. Math. Soc. 74 (1953), 1043. MR 14, 989. MR 0054850 (14:989d)
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 , A wild Cantor set in the Hilbert cube, Pacific J. Math. 24 (1968), 189193. MR 36 #4539. MR 0221487 (36:4539)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002994719710275476X
PII:
S 00029947(1971)0275476X
Keywords:
Invertibleisotopy,
Kcoincident,
Kstationary,
homeomorphism,
propertyZ,
stable homeomorphism extension
Article copyright:
© Copyright 1971
American Mathematical Society
