On the trivial extension of equivalence relations on analytic spaces

Takijima, Kunio; Suzuki, Tetsutaro

doi:10.1090/S0002-9947-1976-0412463-7

On the trivial extension of equivalence relations on analytic spaces
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by Kunio Takijima and Tetsutaro Suzuki PDF

Trans. Amer. Math. Soc. 219 (1976), 369-377 Request permission

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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