Recognizing -manifolds

Author:
James P. Henderson

Journal:
Proc. Amer. Math. Soc. **94** (1985), 721-727

MSC:
Primary 57N20; Secondary 54B15, 54C99, 58B05

MathSciNet review:
792291

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Abstract | References | Similar Articles | Additional Information

Abstract: Denote by the subspace of the Hilbert cube consisting of for all but finitely many }. Then following characterization of manifolds modeled on is proven and applied to cell-like, upper semicontinuous decompositions of -manifolds. An ANR is a -manifold if and only if (a) is the countable union of finite-dimensional compacta, (b) each compact subset of is a strong -set, and (c) for each positive integer , every mapping can be arbitrarily closely approximated by an injection.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0792291-4

Keywords:
Countable dimensional manifold,
cell-like decompositions,
Euclidean injection property

Article copyright:
© Copyright 1985
American Mathematical Society