RT Journal Article
T1 Complexity of global semianalytic sets in a real analytic manifold of dimension 2
A1 Andradas Heranz, Carlos
A1 Díaz-Cano Ocaña, Antonio
AB Let 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.
PB Walter de Gruyter
SN 0075-4102
YR 2001
FD 2001
LK https://hdl.handle.net/20.500.14352/57153
UL https://hdl.handle.net/20.500.14352/57153
LA eng
DS Docta Complutense
RD 17 dic 2025