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arXiv · 1102.3252

$σ$-homogeneity of Borel sets

Alexey Ostrovsky
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Abstract

We give an affirmative answer to the following question: Is any Borel subset of a Cantor set $\textbf{ C}$ a sum of a countable number of pairwise disjoint $h$-homogeneous subspaces that are closed in $X$? It follows that every Borel set $X \subset \textbf{ R}^n$ can be partitioned into countably many $h$-homogeneous subspaces that are $G_δ$-sets in $X$.

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Alexey Ostrovsky. 2011-02-16. $σ$-homogeneity of Borel sets. https://arxiv.org/abs/1102.3252

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