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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

AR-maps obtained from cell-like maps


Authors: George Kozlowski, Jan van Mill and John J. Walsh
Journal: Proc. Amer. Math. Soc. 82 (1981), 299-302
MSC: Primary 54C56; Secondary 54C10, 54C55
DOI: https://doi.org/10.1090/S0002-9939-1981-0609671-6
MathSciNet review: 609671
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Abstract: The recent solution by J. van Mill of a problem of Borsuk involves using a convexification procedure in order to produce a map $ f$ from the Hilbert cube $ Q$ to a non-$ AR$ $ X$ so that each point-inverse $ {f^{ - 1}}(x)$ is a Hilbert cube. A different method of obtaining $ AR$-maps from cell-like maps is described and is used to show that if there is a dimension raising cell-like map, then there is an integer $ n$ and a map $ f$ from $ Q$ to a non-$ AR$ $ X$ so that each point-inverse $ {f^{ - 1}}(x)$ is an $ n$-cell or a point.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0609671-6
Keywords: Cell-like, absolute retract, hereditary shape, equivalence, dimension
Article copyright: © Copyright 1981 American Mathematical Society