Universal cell-like maps
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- by Jerzy Dydak and Jerzy Mogilski PDF
- Proc. Amer. Math. Soc. 122 (1994), 943-948 Request permission
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.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 943-948
- MSC: Primary 55M10; Secondary 54F45
- DOI: https://doi.org/10.1090/S0002-9939-1994-1242080-7
- MathSciNet review: 1242080