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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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  • [BP] C. Bassaga and A. Pelczyński, Selected topics in infinite-dimensional topology, Monogr. Mat. 58, PWN, Warsaw, 1975.
  • [DT] T. Dobrowolski and H. Toruńczyk, Separable complete ANRs admitting a group structure are Hilbert manifolds, Topology Appl. 12 (1981), no. 3, 229–235. MR 623731, 10.1016/0166-8641(81)90001-8
  • [Du] James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
  • [E] James Eells Jr., On the geometry of function spaces, Symposium internacional de topología algebraica International symposium on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, pp. 303–308. MR 0098419
  • [Ge] Ross Geoghegan, On spaces of homeomorphisms, embeddings and functions. I, Topology 11 (1972), 159–177. MR 0295281
  • [Hu] Sze-tsen Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. MR 0181977
  • [Mi] E. Michael, Uniform ARs and ANRs, Compositio Math. 39 (1979), no. 2, 129–139. MR 546964
  • [To$ _{1}$] H. Toruńczyk, Concerning locally homotopy negligible sets and characterization of 𝑙₂-manifolds, Fund. Math. 101 (1978), no. 2, 93–110. MR 518344
  • [To$ _{2}$] H. Toruńczyk, Characterizing Hilbert space topology, Fund. Math. 111 (1981), no. 3, 247–262. MR 611763
  • [To$ _{3}$] H. Toruńczyk, A correction of two papers concerning Hilbert manifolds: “Concerning locally homotopy negligible sets and characterization of 𝑙₂-manifolds” [Fund. Math. 101 (1978), no. 2, 93–110; MR0518344 (80g:57019)] and “Characterizing Hilbert space topology” [ibid. 111 (1981), no. 3, 247–262; MR0611763 (82i:57016)], Fund. Math. 125 (1985), no. 1, 89–93. MR 813992
  • [Ya] Tatsuhiko Yagasaki, Fiber shape theory, Tsukuba J. Math. 9 (1985), no. 2, 261–277. MR 818209

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Keywords: Space of cross sections, locally trivial bundle, ANR, $ {l_2}$-manifold
Article copyright: © Copyright 1988 American Mathematical Society