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Graphs with ∏ 1 0 (K)Y-sections

Graphs with ∏ 1 0 (K)Y-sections We prove that a Borel subset of the product of two internal setsX andY all of whoseY-sections are ∏ 1 0 (K)(∑ 1 0 (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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Graphs with ∏ 1 0 (K)Y-sections

Živaljević, Boško
Archive for Mathematical Logic , Volume 32 (4) – Mar 13, 2005
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References (14)

Publisher
Springer Journals
Copyright
Copyright © 1993 by Springer-Verlag
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/BF01387406
Publisher site
See Article on Publisher Site

Abstract

We prove that a Borel subset of the product of two internal setsX andY all of whoseY-sections are ∏ 1 0 (K)(∑ 1 0 (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.

Journal

Archive for Mathematical Logic – Springer Journals

Published: Mar 13, 2005

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