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

2025/03/18 by Pol, Roman, Reńska, Mirosława
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2503.14235

Abstract

We shall prove that if X, Y are compact metrizable spaces of positive dimension and h: X x Y --> X is a continuous map with zero-dimensional fibers then X contains a non-trivial 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 J. Dudák and B. Vejnar.

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