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Another counterexample in ANR theory


Author: Jan van Mill
Journal: Proc. Amer. Math. Soc. 97 (1986), 136-138
MSC: Primary 55M15; Secondary 54C20
DOI: https://doi.org/10.1090/S0002-9939-1986-0831402-X
MathSciNet review: 831402
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Abstract: We answer an old question due to Kuratowski by constructing a (separable metric) space $ X$ having the following properties: (1) $ X$ is not an ANR, and (2) for every space $ Y$ and for every compact $ A \subseteq Y$, every continuous map $ f:A \to X$ can be continuously extended to a map $ \bar f:Y \to X$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0831402-X
Keywords: Absolute retract, cell-like mapping, Taylor example
Article copyright: © Copyright 1986 American Mathematical Society

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