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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the trivial extension of equivalence relations on analytic spaces


Authors: Kunio Takijima and Tetsutaro Suzuki
Journal: Trans. Amer. Math. Soc. 219 (1976), 369-377
MSC: Primary 32C25; Secondary 32C15
DOI: https://doi.org/10.1090/S0002-9947-1976-0412463-7
MathSciNet review: 0412463
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Abstract: In this paper, we shall consider the problem: let X be a (reduced) analytic space and A a nowhere dense analytic set in X. And let R be a proper equivalence relation on A such that the quotient space $ A/R$ is an analytic space, and $ \tilde R$ the trivial extension of R to X. Then, is $ X/\tilde R$ an analytic space? To this, we have three sufficient conditions. Moreover, using this result we shall extend Satz 1 of H. Kerner [8].


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DOI: https://doi.org/10.1090/S0002-9947-1976-0412463-7
Keywords: Analytic space, proper equivalence relation, trivial extension of equivalence relation
Article copyright: © Copyright 1976 American Mathematical Society