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The space of cross sections of a bundle


Author: Katsuro Sakai
Journal: Proc. Amer. Math. Soc. 103 (1988), 956-960
MSC: Primary 57N20; Secondary 55R10
MathSciNet review: 947690
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947690-7
Keywords: Space of cross sections, locally trivial bundle, ANR, $ {l_2}$-manifold
Article copyright: © Copyright 1988 American Mathematical Society