Basic properties of real analytic and semianalytic germs

Abstract

We give an expository account of the basic features of analytic and semianalytic germs. The main results treated here are Risler's Nullstellensatz, the curve selection lemma and the finiteness theorem for semianalytic germs. The method of proof consists of a real local parametrization theorem and an analytic version of Thom's general lemma. Finally, all these properties suggest that real spectra behave for analytic algebras as properly as for finitely generated algebras over R.