On connected components of some globally semi-analytic sets
  We isolate a class, say $\mathcal{A}$, of global real analytic functions such that, each global semi-analytic set defined by $\mathcal{A}$ has only finitely many connected components and each component is also a global semi-analytic set defined by $\mathcal{A}$. 
Abdelhafed Elkhadiri
math.AG