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

 

Dense sigma-compact subsets of infinite-dimensional manifolds


Author: T. A. Chapman
Journal: Trans. Amer. Math. Soc. 154 (1971), 399-426
MSC: Primary 57.55
MathSciNet review: 0283828
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Abstract: In this paper four classes of separable metric infinite-dimensional manifolds are studied; those which are locally the countable infinite product of lines, those which are locally open subsets of the Hubert cube, and those which are locally one of two dense sigma-compact subsets of the Hilbert cube. A number of homeomorphism, product, characterization, and embedding theorems are obtained concerning these manifolds.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0283828-7
PII: S 0002-9947(1971)0283828-7
Keywords: Fréchet manifold, Hubert cube manifold, compact absorption property, Property Z, infinite deficiency, finite-dimensional compact absorption property
Article copyright: © Copyright 1971 American Mathematical Society