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An alternative approach to the decomposition of functions

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
159
Issue
7
Identifiers
DOI: 10.1016/j.topol.2011.04.032
Keywords
  • Borel-Measurable
  • Open-Borel
  • Countably Continuous
  • Borel Class
  • Open Function
  • Closed Function

Abstract

Abstract Let a function f:X→Y with compact fibers takes any open set into a union of an open and a closed set. Then there exist subsets Tn⊂X (n=1,2,…) such that every restriction f|Tn is open or closed function onto Yn and Yn (n=0,1,…) cover Y. This result is related to the problem of preservation of Borel classes by open-Borel functions and to Luzinʼs question about decomposition of Borel-measurable functions into countably many continuous ones.

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