Acquistapace, FrancescaBroglia, FabrizioFernando Galván, José Francisco2023-06-182023-06-182015-12-170025-583110.1007/s00208-015-1342-5https://hdl.handle.net/20.500.14352/24309In this work we present the concept of C-semianalytic subset of a real analytic manifold and more generally of a real analytic space. C-semianalytic sets can be understood as the natural generalization to the semianalytic setting of global analytic sets introduced by Cartan (C-analytic sets for short). More precisely S is a C-semianalytic subset of a real analytic space (X, OX ) if each point of X has a neighborhood U such that S ∩ U is a finite boolean combinations of global analytic equalities and strict inequalities on X. By means of paracompactness C-emianalytic sets are the locally finite unions of finite boolean combinations of global analytic equalities and strict inequalities on X. The family of C-semianalytic sets is closed.engjournal articlehttp://link.springer.com/article/10.1007%2Fs00208-015-1342-5#page-1http://link.springer.comrestricted access512.7Geometria algebraica1201.01 Geometría Algebraica