$σ$-homogeneity of Borel sets

Details $σ$-homogeneity of Borel sets $σ$-homogeneity of Borel sets

2011-02-16

arxiv.org/abs/1102.3252v1

Mathematics

Logic

4 pages

Scientific paper

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 $G_{\delta}$-sets in $X$.

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