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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A cross section theorem and an application to $ C\sp*$-algebras


Authors: Robert R. Kallman and R. D. Mauldin
Journal: Proc. Amer. Math. Soc. 69 (1978), 57-61
MSC: Primary 28A05; Secondary 46L05
MathSciNet review: 0463390
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Abstract: The purpose of this note is to prove a cross section theorem for certain equivalence relations on Borel subsets of a Polish space. This theorem is then applied to show that cross sections always exist on countably separated Borel subsets of the dual of a separable $ {C^ \ast }$-algebra.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0463390-8
Keywords: Quotient Borel space, Borel cross section, $ {C^ \ast }$-algebra
Article copyright: © Copyright 1978 American Mathematical Society