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

Michal Hevessy

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arXiv · 2411.17573

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

Michal Hevessy

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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.

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BibTeX RIS

Michal Hevessy. 2024-11-26. Zero-dimensional metrizable CDH space $X$ such that $X^2$ is not CDH. https://arxiv.org/abs/2411.17573

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