Semianalytic set

Summary

A semianalytic set is a subset of a real analytic manifold with a simple local description. Near each point it is given by finitely many equations and strict inequalities between real analytic functions. It is the analytic analogue of a semialgebraic set, with polynomials replaced by real analytic functions. Semianalytic sets are locally finite unions of connected real analytic submanifolds, and they can be triangulated. Since images of semianalytic sets under proper analytic maps need not be semianalytic, one also studies the larger class of subanalytic sets.