Deficiency in -manifolds

Author:
William H. Cutler

Journal:
Proc. Amer. Math. Soc. **34** (1972), 260-266

MSC:
Primary 58B05

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 , 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 has an open neighborhood *U* and a homeomorphism such that , (3) each has an open neighborhood *U* and a homeomorphism such that , (4) there is a homeomorphism such that for , (5) *K* is infinite-deficient (i.e. there is a homeomorphism such that , and (6) *K* is the finite union of sets each having one of the above properties.

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Additional Information

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