The space of cross sections of a bundle

Sakai, Katsuro

doi:10.1090/S0002-9939-1988-0947690-7

The space of cross sections of a bundle
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Proc. Amer. Math. Soc. 103 (1988), 956-960 Request permission

Abstract:

Let $B$ be a nondiscrete compactum, $Y$ a separable complete metrizable ANR with no isolated point and $p:X \to B$ a locally trivial bundle with fiber $Y$ admitting a section. It is proved that the space $\Gamma (X)$ of all cross sections of $p:X \to B$ is an ${l_2}$-manifold.

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