Baro González, ElíasMartin Pizarro, Amador2024-10-032024-10-032022-06-01Baro E, Martin-Pizarro A. Open core and small groups in dense pairs of topological structures. Annals of Pure and Applied Logic 2021;172:102858. https://doi.org/10.1016/j.apal.2020.102858.https://doi.org/10.1016/j.apal.2020.102858https://hdl.handle.net/20.500.14352/108621Dense pairs of geometric topological fields have tame open core, that is, every definable open subset in the pair is already definable in the reduct. We fix a minor gap in the published version of van den Dries's seminal work on dense pairs of o-minimal groups, and show that every definable unary function in a dense pair of geometric topological fields agrees with a definable function in the reduct, off a small definable subset, that is, a definable set internal to the predicate. For certain dense pairs of geometric topological fields without the independence property, whenever the underlying set of a definable group is contained in the dense-codense predicate, the group law is locally definable in the reduct as a geometric topological field. If the reduct has elimination of imaginaries, we extend this result, up to interdefinability, to all groups internal to the predicateengAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articlehttps://doi.org/10.1016/j.apal.2020.102858https://www.sciencedirect.com/science/article/abs/pii/S0168007220300828restricted accessÁlgebraLógica simbólica y matemática (Matemáticas)1102.08 Lógica Matemática1201 Álgebra