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Proceedings of the American Mathematical Society

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



A solution to a problem of Eilenberg concerning dimension lowering mappings

Authors: James Keesling and David C. Wilson
Journal: Proc. Amer. Math. Soc. 86 (1982), 159-162
MSC: Primary 54F45; Secondary 54C99
MathSciNet review: 663888
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Abstract: This paper describes a map $ f$ from a metric space $ X$ (having the same dimension at each of its points) onto a space $ Y$ such that $ \dim X > \dim Y > 0$ with the property that $ \dim K \geqslant \dim f(K)$ for every closed set $ K$ contained in $ X$. This answers a question posed by Eilenberg in 1936 in The Scottish Book. This question was answered with a more complicated example by Rubin, Schori, and Walsh.

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Keywords: Dimension, mapping, monotone mapping, cell-like mapping, dimension lowering mapping
Article copyright: © Copyright 1982 American Mathematical Society