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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Deficiency in $F$-manifolds
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by William H. Cutler PDF
Proc. Amer. Math. Soc. 34 (1972), 260-266 Request permission

Abstract:

Let M be a manifold modelled on a metrizable, locally-convex, topological vector space F such that $F \cong {F^\omega }$, and let K be a closed subset of M. Then the following are equivalent: (1) K is locally a subset of a collared submanifold of M, (2) each $x \in K$ has an open neighborhood U and a homeomorphism $h:U \to {l_2} \times F$ such that $h(U \cap K) \subset \{ 0\} \times F$, (3) each $x \in K$ has an open neighborhood U and a homeomorphism $h:U \to F \times F$ such that $h(U \cap K) \subset \{ 0\} \times F$, (4) there is a homeomorphism $h:M \to M \times F$ such that for $x \in K,h(x) = (x,0)$, (5) K is infinite-deficient (i.e. there is a homeomorphism $h:M \to M \times {l_2}$ such that $h(K) \subset M \times \{ 0\} )$, and (6) K is the finite union of sets each having one of the above properties.
References
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 260-266
  • MSC: Primary 58B05
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0298710-5
  • MathSciNet review: 0298710