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PL APPROXIMATIONS OF FIBER PRESERVING HOMEOMORPHISMS OF VECTOR BUNDLES

Tatsuhiko Yagasaki
Tsukuba Journal of Mathematics
Vol. 21, No. 1 (June 1997), pp. 181-198
Stable URL: http://www.jstor.org/stable/43686008
Page Count: 18
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
PL APPROXIMATIONS OF FIBER PRESERVING HOMEOMORPHISMS OF VECTOR BUNDLES
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Abstract

We investigate the group of f.p. homeomorphisms of an n-dimensional vector bundle ξ. In the case n ≥ 5 and the base space of ξ is countable dimensional, we show that every f.p. stable homeomorphism of ξ 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 ξ with the uniform topology has the mapping absorption property for maps from countable dimensional metric spaces into the group of f.p. homeomorphisms of ξ which are PL on the unit open ball.

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