Fernando Galván, José Francisco2023-06-172023-06-172016-080025-587410.1007/s00209-016-1634-9https://hdl.handle.net/20.500.14352/18946Dedicated to Prof. C. Andradas in occasion of his 60th birthday.t In this work we present the concept of amenable C-semianalytic subset of a real analytic manifold M and study the main properties of this type of sets. Amenable C-semianalytic sets can be understood as globally defined semianalytic sets with a neat behavior with respect to Zariski closure. This fact allows us to develop a natural definition of irreducibility and the corresponding theory of irreducible components for amenable Csemianalytic sets. These concepts generalize the parallel ones for: complex algebraic and analytic sets, C-analytic sets, Nash sets and semialgebraic sets.spajournal articlehttp://link.springer.com/article/10.1007%2Fs00209-016-1634-9http://link.springer.comrestricted access512.7C-analytic and C-semianalytic setsAmenable C-semianalytic setsZariski closure · IrreducibilityIrreducible componentsAnalytic normalization.Geometria algebraica1201.01 Geometría Algebraica