Person: Chocano Feito, Pedro José
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First Name
Pedro José
Last Name
Chocano Feito
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Álgebra, Geometría y Topología
Area
Álgebra
Identifiers
13 results
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Now showing 1 - 10 of 13
- Project number: 343
Item Tutoriales guiados de prácticas en “Estadística: Análisis de Datos e Inferencia” mediante el software libre SAS University Edition(2020) Martín Apaolaza, Nirian; Castilla González, Elena María; Chocano Feito, Pedro José; Jaenada Malagón, María; Pardo Llorente, Leandro Item Computational methods in topology and dynamical systems(2022) Chocano Feito, Pedro José; Alonso Morón, Manuel; Romero Ruiz del Portal, FranciscoItem A combinatorial description of shape theory() Chocano Feito, Pedro José; Alonso Morón, Manuel; Romero Ruiz Del Portal, FranciscoWe give a combinatorial description of shape theory using finite topological T0-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse sequences of finite spaces and prove some properties.Item Characteristic Curves and the exponentiation in the Riordan Lie group: A connection through examples(2022) Chocano Feito, Pedro José; Luzón, Ana; Alonso Morón, Manuel; Prieto Martínez, Luis FelipeWe point out how to use the classical characteristic method, that is used to solve quasilinear PDE's, to obtain the matrix exponential of some lower triangle infinite matrices. We use the Lie Frechet structure of the Riordan group described in [4]. After that we describe some linear dynamical systems in K[[x]] with a concrete involution being a symmetry or a time-reversal symmetry for them. We take this opportunity to assign some dynamical properties to the Pascal Triangle.Item Coincidence theorems for finite topological spaces() Chocano Feito, Pedro José; Alonso Morón, Manuel; Romero Ruiz Del Portal, FranciscoWe adapt the definition of the Vietoris map to the framework of finite topological spaces and we prove some coincidence theorems. From them, we deduce a Lefschetz fixed point theorem for multivalued maps that improves recent results in the literature. Finally, it is given an application to the approximation of discrete dynamical systems in polyhedra.Item Computational approximations of compact metric spaces(Physica D: nonlinear phenomena, 2022) Chocano Feito, Pedro José; Alonso Morón, Manuel; Romero Ruiz Del Portal, FranciscoGiven a compact metric space X, we associate to it an inverse sequence of finite T0 topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of X that is a strong deformation retract. We provide a method to approximate the homology groups of X and other algebraic invariants. Finally, we study computational aspects and the implementation of this method.Item On some topological realizations of groups and homomorphisms(Transactions of the American Mathematical Society, 2022) Chocano Feito, Pedro José; Alonso Morón, Manuel; Romero Ruiz Del Portal, FranciscoGiven a homomorphism of groups f : G → H, we construct a topological space Xf such that its group of homeomorphisms Aut(Xf) is isomorphic to G, its group of homotopy classes of self-homotopy equivalences E(Xf) is isomorphic to H and the natural map between Aut(Xf) and E(Xf) is f. In addition, we consider realization problems involving homology groups, homotopy groups and groups of automorphisms.Item On the triviality of flows in Alexandroff spaces(2022) Chocano Feito, Pedro José; Alonso Morón, Manuel; Romero Ruiz Del Portal, FranciscoWe prove that the unique possible flow in an Alexandroff T0-space is the trivial one. On the way of motivation, we relate Alexandroff spaces with topological hyperspaces.Item Topological realizations of groups in Alexandroff spaces(Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020) Chocano Feito, Pedro José; Alonso Morón, Manuel; Romero Ruiz Del Portal, FranciscoGiven a group G, we provide a constructive method to get infinitely many (non-homotopy-equivalent) Alexandroff spaces, such that the group of autohomeomorphisms, the group of homotopy classes of self-homotopy equivalences and the pointed version are isomorphic to G. As a result, any group G can be realized as the group of homotopy classes of self-homotopy equivalences of a topological space X, for which there exists a CW complex K(X) and a weak homotopy equivalence from K(X) to X.Item Shape compacta as extension of weak homotopy of finite spaces(2022) Chocano Feito, Pedro José; Alonso Morón, Manuel; Romero Ruiz Del Portal, FranciscoWe construct a category that classifes compact Hausdorff spaces by their shape and fnite topological spaces by their weak homotopy type.