On normal analytic sets, II
Ikuo Kimura · Proceedings of the Japan Academy Series A Mathematical Sciences · 1967
I have studied conditions for an analytic set being normal and obtained the following _1. ) Theorem 1.If , is normal at O, then , satisfies the condi- tions () and ().Moreover, when V, is principal, , is normal at 0 if and only if , satisfies the conditions (e) and ().The two conditions in Theorem i are the following.Condition (a). ) Let (x , y0) be a point sufficiently near 0, such that (x)ve0, f(x , y)-O.Let ()(x y)-.c ( ' " zz--z".)(x)(y--(x)) l</<e, l<i<, 1-----0 be the systems of Puiseux-series, attached to (x , yO).Then, for i, j, ij, there exists an index [, l<g<e, such that we have C(o ,, .(xO)c,o Condition (B).Let (x , yO) be a point sufficiently near O, such that (x) O, f(x , yO) O. Let z, z,(x.y) .c")(x)(y-(x)).1 < < e. y-'-O