Zero-dimensional metrizable CDH space $X$ such that $X^2$ is not CDH

Michal Hevessy

Zero-dimensional metrizable CDH space $X$ such that $X^2$ is not CDH

General Topology 2024-11-27 v1

Authors: Michal Hevessy

Abstract

In this paper a construction of a metrizable zero-dimensional CDH space $X$ such that $X^2$ has exactly $\mathfrak{c}$ countable dense subsets is provided. Furthermore, it is shown that the space can be constructed consistently co-analytic. Thus answering an open question asked by Medini. To do so we use the notion of $\lambda$ -sets.

Keywords

general topology metric spaces topological spaces

Cite

@article{arxiv.2411.17573,
  title  = {Zero-dimensional metrizable CDH space $X$ such that $X^2$ is not CDH},
  author = {Michal Hevessy},
  journal= {arXiv preprint arXiv:2411.17573},
  year   = {2024}
}

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5 pages

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