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 | References | Similar Articles | Additional Information
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