Manifolds modelled on or bounded weak-* topologies

Author:
Richard E. Heisey

Journal:
Trans. Amer. Math. Soc. **206** (1975), 295-312

MSC:
Primary 58B05; Secondary 58C20

DOI:
https://doi.org/10.1090/S0002-9947-1975-0397768-X

MathSciNet review:
0397768

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Abstract: Let , and let denote the conjugate, , of a separable, infinite-dimensional Banach space with its bounded weak- topology. We investigate properties of paracompact, topological manifolds modelled on , where is either or . Included among our results are that locally trivial bundles and microbundles over with fiber are trivial; there is an open embedding ; and if and have the same homotopy type, then and are homeomorphic. Also, if is an open subset of , then is homeomorphic to . Thus, two open subsets of are homeomorphic if and only if they have the same homotopy type. Our theorems about -manifolds, as above, immediately yield analogous theorems about -manifolds, where is a separable, reflexive, infinite-dimensional Banach space with its bounded weak topology.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1975-0397768-X

Keywords:
Bounded weak- topology,
manifold,
Banach space,
topological vector space,
direct limit,
Hilbert cube,
microbundle,
bundle,
stable classification

Article copyright:
© Copyright 1975
American Mathematical Society