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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Hereditary ball-covers for some Banach manifolds

Author: James E. West
Journal: Proc. Amer. Math. Soc. 33 (1972), 132-136
MSC: Primary 57A20
MathSciNet review: 0336747
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Abstract: At a problem seminar in Ithaca, New York, during January 1969, James Eells raised the question (numbered 33 on the circulated list) of whether a paracompact Fréchet manifold admits a locally finite cover by open sets, all of whose intersections are contractible. This had been established in the separable case by David Henderson, who obtained star-finite covers. This note settles the case that the model space is a Banach space homeomorphic to its countably infinite Cartesian power. The cover elements and all nonempty intersections are homeomorphic to the model. A short proof that the nerve of the cover has the homotopy type of the manifold is also included.

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Keywords: Banach manifold, locally-finite cover, nerve, homotopy type
Article copyright: © Copyright 1972 American Mathematical Society