Infinite deficiency in Fréchet manifolds

Author:
T. A. Chapman

Journal:
Trans. Amer. Math. Soc. **148** (1970), 137-146

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:
https://doi.org/10.1090/S0002-9947-1970-0256418-9

Keywords:
The Hilbert cube,
Fréchet manifolds,
Property *Z*,
infinite deficiency

Article copyright:
© Copyright 1970
American Mathematical Society