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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Products of complexes and Fréchet spaces which are manifolds


Author: James E. West
Journal: Trans. Amer. Math. Soc. 166 (1972), 317-337
MSC: Primary 58B05
MathSciNet review: 0293679
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Abstract: It is shown that if a locally finite-dimensional simplicial complex is given the ``barycentric'' metric, then its product with any Fréchet space X of suitably high weight is a manifold modelled on X, provided that X is homeomorphic to its countably infinite Cartesian power. It is then shown that if X is Banach, all paracompact X-manifolds may be represented (topologically) by such products.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0293679-6
PII: S 0002-9947(1972)0293679-6
Keywords: Fréchet manifold, Banach manifold, metric simplicial complex, homotopy type
Article copyright: © Copyright 1972 American Mathematical Society