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No product of two nontrivial countable-dimensional continua maps lightly into any of the factors

Part of: Spaces with richer structures Special properties

Published online by Cambridge University Press:  07 August 2025

Roman Pol Open the ORCID record for Roman Pol [Opens in a new window]  and
Mirosława Reńska Open the ORCID record for Mirosława Reńska [Opens in a new window]
Roman Pol
Affiliation:
Institute of Mathematics, University of Warsaw, Warszawa 02-097, Poland e-mail: r.pol@mimuw.edu.pl
Mirosława Reńska*
Affiliation:
Faculty of Mathematics and Information Science, Warsaw University of Technology, Warszawa 00-662, Poland
*
e-mail: miroslawa.renska@pw.edu.pl
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Abstract

We shall prove that if X, Y are compact metrizable spaces of positive dimension and ${h:X\times Y \to X}$ is a continuous map with zero-dimensional fibers then X contains a nontrivial continuum without one-dimensional subsets; in particular, X is not a countable union of zero-dimensional sets, which provides a negative answer to a question of Dudák and Vejnar [DV]

Keywords

Compact spacecountable-dimensional spacelight maptopological product

MSC classification

Primary: 54F45: Dimension theory 54F15: Continua and generalizations 54E45: Compact (locally compact) metric spaces

Information

Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 6
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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