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Graphs with ∏ 01 (K)Y-sections

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Summary

We prove that a Borel subset of the product of two internal setsX andY all of whoseY-sections are ∏ 01 (K)(∑ 01 (K)) sets is the intersection (union) of a countable sequence of Borel graphs with internalY-sections. As a consequence we prove some standard results about the domains of graphs in the product of two topological spaces all of whose horizontal section are compact (open) sets. A version of classical Vitali-Lusin theorem for those types of graphs is given as well as a new proof (and an extension) of a classical result of Kunugui.

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Author notes

  1. Boško Živaljević

    Present address: Department of Computer Science, The University of Illinois at Urbana-Champaign, 61801, Urbana, IL, USA

Authors and Affiliations

  1. Department of Computer Science, Michigan State University, 48823, East Lansing, MI, USA

    Boško Živaljević

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  1. Boško Živaljević
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Dedicated to the meamory of Goran Krkić

1980 Mathematics Subject Classification (1985) Revision). Primary 03H05. Secondary 04A15, 54H05

Research supported by the Serbian Science Foundation through a grant from the Mathematical Institute in Belgrade, Yugoslavia

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Živaljević, B. Graphs with ∏ 01 (K)Y-sections. Arch Math Logic 32, 259–273 (1993). https://doi.org/10.1007/BF01387406

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  • DOI: https://doi.org/10.1007/BF01387406

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