Borel sets and functions in topological space

Abstract

We present a construction of the Borel hierarchy in general topological spaces and its relation to Baire hierarchy. We define mappings of Borel class, prove the validity of the Lebesgue–Hausdorff–Banach characterization for them and show their relation to Baire classes of mappings on compact spaces.

Keywords

• Borel sets
• Borel functions