Borel sets and functions in topological spaces

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 α, prove the validity of the Lebesgue-Hausdor-Banach characterization for them and show their relation to Baire classes of mappings on compact spaces. The obtained results are used for studying Baire and Borel order of compact spaces, answering thus one part of a question raised by R. D. Mauldin. We present several examples showing some natural limits of our results in non-compact spaces.