Baro González, ElíasPalacín Cruz, Daniel2024-10-032024-10-032024-01-15Baro E, Palacín D. Ellis enveloping semigroups in real closed fields. Rev Real Acad Cienc Exactas Fis Nat Ser A-Mat 2024;118:69. https://doi.org/10.1007/s13398-024-01562-7.10.1007/s13398-024-01562-7https://hdl.handle.net/20.500.14352/108622We introduce the Boolean algebra of d-semialgebraic (more generally, d-definable) sets and prove that its Stone space is naturally isomorphic to the Ellis enveloping semigroup of the Stone space of the Boolean algebra of semialgebraic (definable) sets. For definably connected o-minimal groups, we prove that this family agrees with the one of externally definable sets in the one-dimensional case. Nonetheless, we prove that in general these two families differ, even in the semialgebraic case over the real algebraic numbers. On the other hand, in the semialgebraic case we characterise real semialgebraic functions representing Boolean combinations of d-semialgebraic setsengAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://doi.org/10.1007/s13398-024-01562-7open accessÁlgebraLógica simbólica y matemática (Matemáticas)Topología1102.08 Lógica Matemática12 Matemáticas