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Baro González, Elías ; Fernando Galván, José Francisco ; Ruiz Sancho, Jesús María | Elsevier | 2014-09This paper is devoted to the approximation of differentiable semialgebraic functions by Nash functions. Approximation by Nash functions is known for semialgebraic functions defined on an affine Nash manifold M, and here we extend it to functions[...]texto impreso
Baro González, Elías ; Berarducci, Alessandro ; Otero, Margarita | London Mathematical Society | 2019-10-01Let G be a group definable in an o-minimal structure M. We prove that the union of the Cartan subgroups of G is a dense subset of G. When M is an expansion of a real closed field we give a characterization of Cartan subgroups of G via their Lie [...]texto impreso
In this short note we show that we must replace the notion of connectedness used in the second author's paper cited in the heading. In particular, we show that with the current notion of connectedness some statements are false.texto impreso
Gómez-Chacón, Inés María ; Baro González, Elías ; Barbero, Marta ; Capel Cuevas, Ángela ; Caravantes Tortajada, Jorge ; Contreras Tejada, Patricia ; Díaz-Cano Ocaña, Antonio ; Folgueira López, Marta ; Gómez Castro, David ; González Prieto, José Ángel ; González Ortega, Jorge ; Ivorra Benjamín, Pierre Paul ; Juan Llamas, María del Carmen ; Melle Hernández, Alejandro ; Pe Pereira, María ; Prieto Yerro, María Ángeles ; Sánchez Benito, María Mercedes ; Ramos del Olmo, Ángel Manuel | 2019-06-24Preparar al profesorado novel de matemáticas para una docencia universitaria de calidad, mediante el desarrollo de competencias y conocimiento estratégico para aprender a enseñar Matemáticas. Se desarrollan ejemplificaciones para ser implementadas.texto impreso
Escribano Martínez, Jesús ; Carmona Ruber, Jorge ; Valdés Morales, Antonio ; Baro González, Elías ; Caravantes Tortajada, Jorge ; Claramunt Pérez, Juan Andrés ; Fernández Rodríguez, María Pilar ; Bellido Terrones, María Luz Divina | 2017-06-30Difusión, entre los estudiantes y los profesores de la Facultad de Matemáticas de la UCM, de herramientas de software libre en las labores académica. En particular, abogamos por el uso de SAGE (www.sagemath.org).texto impreso
In [E. Baro, M. Otero, On o-minimal homotopy, Quart. J. Math. (2009) 15pp, in press (doi:10.1093/qmath/hap011)] o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead th[...]texto impreso
These are the (informal and expanded) notes of a mini-course given in the Universidad Autónoma de Madrid, 29-30 of May 2018 (6 hours). The mini-course was given at the end of a master course on Model Theory with applications to Algebra. The purp[...]texto impreso
Let R be an o-minimal structure over a real closed field R. Given a simplicial complex K and some definable subsets S1, . . . , Sl of its realization |K| in R we prove that there exist a subdivision K0 of K and a definable triangulation '0: |K0|[...]texto impreso
We work over an o-minimal expansion of a real closed field. The o-minimal homotopy groups of a definable set are defined naturally using definable continuous maps. We prove that any two semialgebraic maps which are definably homotopic are also s[...]texto impreso
We introduce the o-minimal LS-category of definable sets in o-minimal expansions of ordered fields and we establish a relation with the semialgebraic and the classical one. We also study the o-minimal LS-category of definable groups. Along the w[...]texto impreso
In this note, we prove that every definably connected, definably compact abelian definable group G in an o-minimal expansion of a real closed field with dim(G)?4 is definably homeomorphic to a torus of the same dimension. Moreover, in the semial[...]
