σ-homogeneity of Borel sets

2011/02/16 by Alexey Ostrovsky, Ostrovsky, Alexey
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Equations Stability Results #General Topology (math.GN) #Logic (math.LO) #Mathematical Dynamics and Fractals #math.GN #math.LO

paper · pdf · doi:10.48550/arxiv.1102.3252

4 pages

arxiv created 2011/02/16 · openalex publication_date 2011/02/16 · arxiv updated 2011/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 ⊂ Rⁿ can be partitioned into countably many h-homogeneous subspaces that are G_δ-sets in X.

Related

• Every finite-dimensional analytic space is σ-homogeneous
• Metrizable DH-spaces of the first category
• Sums of two homogeneous Cantor sets
• Generalized Cantor manifolds and homogeneity
• Products and h-homogeneity