Characterizing the topology of infinite-dimensional -compact manifolds

Author:
Jerzy Mogilski

Journal:
Proc. Amer. Math. Soc. **92** (1984), 111-118

MSC:
Primary 57N20; Secondary 54C55

DOI:
https://doi.org/10.1090/S0002-9939-1984-0749902-8

MathSciNet review:
749902

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Abstract: A metric space , which is a countable union of finite-dimensional compacta, is a manifold modelled on the space all but finitely many iff is an ANR and the following condition holds: given , a pair of finite-dimensional compacta and a map such that is an embedding, there is an embedding such that and for all . An analogous condition characterizes manifolds modelled on the space .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1984-0749902-8

Keywords:
Sigma-compact metric ANR's,
the strong universality property for compacta,
infinite-dimensional sigma-compact manifolds,
-sets,
near-homeomorphisms

Article copyright:
© Copyright 1984
American Mathematical Society