## Tsukuba Journal of Mathematics

### PL approximations of fiber preserving homeomorphisms of vector bundles

Tatsuhiko Yagasaki

#### 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.

#### Article information

Source
Tsukuba J. Math., Volume 21, Number 1 (1997), 181-198.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496163170

Digital Object Identifier
doi:10.21099/tkbjm/1496163170

Mathematical Reviews number (MathSciNet)
MR1467230

Zentralblatt MATH identifier
0884.57021

#### Citation

Yagasaki, Tatsuhiko. PL approximations of fiber preserving homeomorphisms of vector bundles. Tsukuba J. Math. 21 (1997), no. 1, 181--198. doi:10.21099/tkbjm/1496163170. https://projecteuclid.org/euclid.tkbjm/1496163170