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June 1997 PL approximations of fiber preserving homeomorphisms of vector bundles
Tatsuhiko Yagasaki
Tsukuba J. Math. 21(1): 181-198 (June 1997). DOI: 10.21099/tkbjm/1496163170

Abstract

We investigate the group of f.p. homeomorphisms of an $n$-dimensional vector bundle $\xi$. In the case $n\geq 5$ and the base space of $\xi$ is countable dimensional, we show that every f.p. stable homeomorphism of $\xi$ can be approximated by f.p. $PL$ homeomorphisms with respect to the majorant topology. As an application we can show that if the base space is compact, then the group of f.p. $PL$ homeomorphisms of $\xi$ with the uniform topology has the mapping absorption property for maps from countable dimensional metric spaces into the group of f.p. homeomorphisms of $\xi$ which are PL on the unit open ball.

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Tatsuhiko Yagasaki. "PL approximations of fiber preserving homeomorphisms of vector bundles." Tsukuba J. Math. 21 (1) 181 - 198, June 1997. https://doi.org/10.21099/tkbjm/1496163170

Information

Published: June 1997
First available in Project Euclid: 30 May 2017

zbMATH: 0884.57021
MathSciNet: MR1467230
Digital Object Identifier: 10.21099/tkbjm/1496163170

Rights: Copyright © 1997 University of Tsukuba, Institute of Mathematics

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Vol.21 • No. 1 • June 1997
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