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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Universal cell-like maps


Authors: Jerzy Dydak and Jerzy Mogilski
Journal: Proc. Amer. Math. Soc. 122 (1994), 943-948
MSC: Primary 55M10; Secondary 54F45
MathSciNet review: 1242080
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Abstract: The main results of the paper are the following:

Theorem. Suppose $ n \leq \infty $. There is a cell-like map $ f:X \to Y$ of complete and separable metric spaces such that $ \dim X \leq n$, and for any cell-like map $ f' :X' \to Y' $ of (complete) separable metric spaces with $ \dim X' \leq n$ there exist (closed) embeddings $ i:Y' \to Y$ and $ j:X' \to {f^{ - 1}}(i(Y' ))$ such that $ fj = if' $.

Corollary. Suppose $ n < \infty $. There is a complete and separable metric space Y such that $ {\dim _{\mathbf{Z}}}Y \leq n$, and any (complete) separable metric space $ Y' $ with $ {\dim _{\mathbf{Z}}}Y' \leq n$ embeds as a (closed) subset of Y.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1242080-7
PII: S 0002-9939(1994)1242080-7
Keywords: Dimension, cohomological dimension, absolute extensors, universal spaces, compactifications, cell-like maps
Article copyright: © Copyright 1994 American Mathematical Society