Submission date: 8 February 2020

Abstract:

Journal-ref: Archiv der Mathematik, vol.109 (2017), pp.529-538

We consider a global semianalytic set defined by real analytic functions definable in an o-minimal structure. When the o-minimal structure is polynomially bounded, we show that the closure of this set is a global semianalytic set defined by definable real analytic functions. We also demonstrate that a connected component of a planar global semianalytic set defined by real analytic functions definable in a substructure of the restricted analytic field is a global semianalytic set defined by definable real analytic functions.

Mathematics Subject Classification: Primary 03C64, Secondary 14P15

Keywords and phrases:

Full text arXiv 2002.03083: pdf, ps.