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Proceedings of the American Mathematical Society

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

 

 

A selector for equivalence relations with $ G\sb{\delta }$ orbits


Author: Douglas E. Miller
Journal: Proc. Amer. Math. Soc. 72 (1978), 365-369
MSC: Primary 54H05
MathSciNet review: 0515142
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Abstract: Assume X is a Polish space and E is an open equivalence on X such that every equivalence class is a $ {G_\delta }$ set. We show that there is a $ {G_\delta }$ transversal for E. It follows that for any separable $ {C^\ast}$-algebra A, there is a Borel cross-section for the canonical map $ {\text{Irr}}(A) \to {\text{Prim}}(A)$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0515142-8
Keywords: Polish space, open equivalence, selector, $ {C^\ast}$-algebra
Article copyright: © Copyright 1978 American Mathematical Society