Abstract
We give an affirmative answer to the following question: Is any Borel subset of a Cantor set C a sum of a countable number of pairwise disjoint h-homogeneous subspaces that are closed in X? It follows that every Borel set \({X \subset {\bf R}^n}\) can be partitioned into countably many h-homogeneous subspaces that are G δ -sets in X.
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Ostrovsky, A. σ-Homogeneity of Borel sets. Arch. Math. Logic 50, 661–664 (2011). https://doi.org/10.1007/s00153-011-0239-6
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DOI: https://doi.org/10.1007/s00153-011-0239-6