This article is cited in 6 papers

Classification of Borel sets and functions for an arbitrary space

V. K. Zakharov^a, T. V. Rodionov<sup>b

a</sup> Centre for New Information Technologies, Moscow State University
^b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: For Borel functions on a perfect normal space and a perfect topological space there are two Baire convergence classifications: one due to Lebesgue and Hausdorff and the other due to Banach. However, neither classification is valid for an arbitrary topological space. In this paper the Baire convergence classification of Borel functions on an arbitrary space is given. This classification of Borel functions uses two classifications of Borel sets: one generalises the Young-Hausdorff classification for a perfect space and the other is new.
Bibliography: 17 titles.

UDC: 517.517+510.225+517.518.26

MSC: Primary 26A21; Secondary 54C50, 54H05, 03E15

Received: 26.02.2007 and 04.10.2007

DOI: 10.4213/sm3845

 English version: Sbornik: Mathematics, 2008, 199:6, 833–869

Bibliographic databases:

• 
• 
• 
• 
•