X⊆R^n is semianalytic if, for all x element R^n, there is an open neighborhood U of x such that X intersection U is a finite Boolean combination of sets {x^_ element U:f(x^_) = 0} and {x^_ element U:g(x^_)>0}, where f, g:U->R are analytic.

analytic function | pseudoanalytic function | subanalytic