$\sigma$-homogeneity of Borel sets
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 $X$.
Comment: 4 pages
Determinacy principles, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Borel sets, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Wadge hierarchy, Mathematics - Logic, \(h\)-homogeneous spaces, Descriptive set theory, Mathematics - General Topology
Determinacy principles, Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets), Borel sets, Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets, Wadge hierarchy, Mathematics - Logic, \(h\)-homogeneous spaces, Descriptive set theory, Mathematics - General Topology
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