Andradas Heranz, CarlosDíaz-Cano Ocaña, Antonio2023-06-202023-06-2020010075-410210.1515/crll.2001.042https://hdl.handle.net/20.500.14352/57153Let X subset of R-n be a real analytic manifold of dimension 2. We study the stability index of X, s(X), that is the smallest integer s such that any basic open subset of X can be written using s global analytic functions. We show that s(X) = 2 as it happens in the semialgebraic case. Also, we prove that the Hormander-Lojasiewicz inequality and the Finiteness Theorem hold true in this context. Finally, we compute the stability index for basic closed subsets, S, and the invariants t and (t) over bar for the number of unions of open (resp. closed) basic sets required to describe any open (resp. closed) global semianalytic set.engjournal articlehttp://www.degruyter.com/view/j/crllopen access512.7Geometria algebraica1201.01 Geometría Algebraica