Hokkaido Mathematical Journal

FUJITA Masato,

On the connected components of a global semianalytic subset of an analytic surface.

Hokkaido Mathematical Journal, 35 (2006) pp.155-179

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Abstract

A global semianalytic subset of a real analytic manifold is a finite union of finite intersections of the solutions of equations and inequalities of real analytic functions on the manifold. Is a union of connected components of a global semianalytic set again global semianalytic? We consider a two-dimensional global semianalytic set such that the normalization of the Zariski closure of it is affine. We show that a union of connected components of it is again global semianalytic. We also give some partial results on connected components of global semianalytic subset of a three-dimensional analytic manifold.

MSC(Primary)14P15
MSC(Secondary)13J30
Uncontrolled KeywordsGlobal Semianalytic Set