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On Paracompact Subsets of Linear Topological Spaces
Richard A. Graff
Proceedings of the American Mathematical Society
Vol. 53, No. 2 (Dec., 1975), pp. 361-366
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2040014
Page Count: 6
You can always find the topics here!Topics: Topological spaces, Mathematical manifolds, Topological theorems, Differential topology, Banach space, Function spaces, Differentiable manifolds, General topology, Functional analysis
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It is shown that a connected open subset of a σ-compact topological space is paracompact in the relative topology only if the subspace is σ-compact. An application is made to demonstrate the existence of nonparacompact open subspaces, in the weak-star and bounded weak-star topologies, of the dual to a nonseparable Banach space. As a corollary, nonempty paracompact manifolds modeled on such a space always have open submanifolds which are not paracompact.
Proceedings of the American Mathematical Society © 1975 American Mathematical Society