Infinite deficiency in Fréchet manifolds
Author:
T. A. Chapman
Journal:
Trans. Amer. Math. Soc. 148 (1970), 137146
MSC:
Primary 57.55; Secondary 54.00
MathSciNet review:
0256418
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Abstract: Denote the countable infinite product of lines by s, let X be a separable metric manifold modeled on s, and let K be a closed subset of X having Property Z in X, i.e. for each nonnull, homotopically trivial, open subset U of X, it is true that is nonnull and homotopically trivial. We prove that there is a homeomorphism h of X onto such that projects onto a single point in each of infinitely many different coordinate directions in s. Using this we prove that there is an embedding of X as an open subset of s such that K is carried onto a closed subset of s having Property Z in s. We also establish stronger versions of these results.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197002564189
PII:
S 00029947(1970)02564189
Keywords:
The Hilbert cube,
Fréchet manifolds,
Property Z,
infinite deficiency
Article copyright:
© Copyright 1970
American Mathematical Society
