Geodesic
On $n$-thin dense sets in powers of topological spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 1, pp. 73-82.

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A subset of a product of topological spaces is called $n$-thin if every its two distinct points differ in at least $n$ coordinates. We generalize a construction of Gruenhage, Natkaniec, and Piotrowski, and obtain, under CH, a countable $T_3$ space $X$ without isolated points such that $X^n$ contains an $n$-thin dense subset, but $X^{n + 1}$ does not contain any $n$-thin dense subset. We also observe that part of the construction can be carried out under MA.
DOI : 10.14712/1213-7243.2015.148
Classification : 54A35, 54B10
Keywords: dense set; thin set; $\kappa $-thin set; independent family 
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Bartoš, Adam. On $n$-thin dense sets in powers of topological spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 57 (2016) no. 1, pp. 73-82. doi : 10.14712/1213-7243.2015.148. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.148/

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