Geodesic
Zero-dimensional metrizable CDH space X such that $X^2$ is not CDH
Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 725-728

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DOI

In this article, a construction of a metrizable zero-dimensional CDH space X such that $X^2$ has exactly $\mathfrak {c}$ many types of 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 a $\lambda $-set.
DOI : 10.4153/S0008439525000062
Mots-clés : Countable dense homogeneous, λ-set, metrizable, zero-dimensional 
Hevessy, Michal. Zero-dimensional metrizable CDH space X such that $X^2$ is not CDH. Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 725-728. doi: 10.4153/S0008439525000062
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     author = {Hevessy, Michal},
     title = {Zero-dimensional metrizable {CDH} space {X} such that $X^2$ is not {CDH}},
     journal = {Canadian mathematical bulletin},
     pages = {725--728},
     year = {2025},
     volume = {68},
     number = {3},
     doi = {10.4153/S0008439525000062},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439525000062/}
}
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