Another counterexample in ANR theory

van Mill, Jan

doi:10.1090/S0002-9939-1986-0831402-X

Another counterexample in ANR theory
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by Jan van Mill

Proc. Amer. Math. Soc. 97 (1986), 136-138

DOI: https://doi.org/10.1090/S0002-9939-1986-0831402-X

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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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Images of ANR’s

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