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On $n$ -thin dense sets in powers of topological spaces

Adam Bartoš — 2016

Commentationes Mathematicae Universitatis Carolinae

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.

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On n -thin dense sets in powers of topological spaces

On $n$ -thin dense sets in powers of topological spaces