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Proceedings of the American Mathematical Society

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

 
 

 

Deficiency in $ F$-manifolds


Author: William H. Cutler
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
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0298710-5
Keywords: Infinite-dimensional manifold, deficiency, negligibility, variable product
Article copyright: © Copyright 1972 American Mathematical Society

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