Locally-trivial bundles and microbundles with infinite-dimensional fibers
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- by T. A. Chapman PDF
- Proc. Amer. Math. Soc. 37 (1973), 595-602 Request permission
Abstract:
The object of this note is to establish trivialization theorems for locally-trivial bundles and microbundles in which the fiber is any one of a large class of infinite-dimensional topological vector spaces and the base space is any paracompact space. These theorems generalize results of Henderson and Wong.References
- R. D. Anderson, Hilbert space is homeomorphic to the countable infinite product of lines, Bull. Amer. Math. Soc. 72 (1966), 515–519. MR 190888, DOI 10.1090/S0002-9904-1966-11524-0
- C. Bessaga and M. I. Kadec, On topological classification of non-separable Banach spaces, Symposium on Infinite-Dimensional Topology (Louisiana State Univ., Baton Rouge, La., 1967) Ann. of Math. Studies, No. 69, Princeton Univ. Press, Princeton, N. J., 1972, pp. 15–24. MR 0417765
- T. A. Chapman, Deficiency in infinite-dimensional manifolds, General Topology and Appl. 1 (1971), 263–272. MR 322898
- David W. Henderson, Micro-bundles with infinite-dimensional fibers are trivial, Invent. Math. 11 (1970), 293–303. MR 282380, DOI 10.1007/BF01403183
- David W. Henderson, Corrections and extensions of two papers about infinite-dimensional manifolds, General Topology and Appl. 1 (1971), 321–327. MR 293677
- David W. Henderson, Stable classification of infinite-dimensional manifolds by homotopy-type, Invent. Math. 12 (1971), 48–56. MR 290413, DOI 10.1007/BF01389826
- James E. West, Fixed-point sets of transformation groups on infinite-product spaces, Proc. Amer. Math. Soc. 21 (1969), 575–582. MR 239588, DOI 10.1090/S0002-9939-1969-0239588-5
- Raymond Y. T. Wong, On homeomorphisms of certain infinite dimensional spaces, Trans. Amer. Math. Soc. 128 (1967), 148–154. MR 214040, DOI 10.1090/S0002-9947-1967-0214040-4 —, On homeomorphisms of infinite-dimensional bundles. I (preprint).
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 37 (1973), 595-602
- MSC: Primary 57A20; Secondary 55F60
- DOI: https://doi.org/10.1090/S0002-9939-1973-0312524-X
- MathSciNet review: 0312524