On the trivial extension of equivalence relations on analytic spaces

Kunio Takijima, Tetsutaro Suzuki
1976 Transactions of the American Mathematical Society  
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 R the trivial extension of R to X. Then, is X/R an analytic space? To this, we have three sufficient conditions. Moreover, using this result we shall extend Satz 1 of H. Kerner [8] .
doi:10.1090/s0002-9947-1976-0412463-7 fatcat:awtamf3yibdhfgjoxqzgxx7o3e