Now showing items 1-12 of 12

    • IconLa categoría de Lusternik-Schnirelmann de los espacios finitos. Enunciado y discusión de un problema  [Final Degree Work]

      Pavón Díaz, Álvaro (2016)
      El trabajo presenta el invariante homotópico conocido como categoría de Lusternik-Schnirelmann (categoría LS, para simplificar) para espacios finitos. La topología y homotopía de estos espacios se resumen en un capítulo ...
    • IconCounting excellent discrete Morse functions on compact orientable surfaces  [Article]

      Ayala Gómez, Rafael; Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio (Universidad de Sevilla, 2010)
      We obtain the number of non-homologically equivalent excellent discrete Morse functions defined on compact orientable surfaces. This work is a continuation of the study which has been done in [2, 4] for graphs.
    • IconCritical elements of proper discrete Morse functions  [Article]

      Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio (Editorial Board of Mathematica Pannonica, 2008)
      The aim of this paper is to study the notion of critical element of a proper discrete Morse function defined on non-compact graphs and surfaces. It is an extension to the non-compact case of the concept of critical simplex ...
    • IconDesigualdades de Morse generalizadas sobre grafos  [Presentation]

      Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio (Alberto Márquez, 2002)
    • IconDiscrete Morse inequalities on infinite graphs  [Article]

      Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio; Ayala Gómez, Rafael (2009)
    • IconEspacios pretopológicos: algunas aplicaciones  [Final Degree Work]

      González Puntas, Gloria (2018)
      The goal of this work is to study the theory of pretopological spaces and some applications. Starting with the key notion of preclosure operator, we will introduce the basic concepts and results, which generalize the ideas ...
    • IconFunciones de Morse discretas sobre complejos infinitos  [Doctoral Thesis]

      Vilches Alarcón, José Antonio (2003)
      Esta memoria está dedicada a la extensión para complejos simpliciales infinitos de los conceptos y resultados de la teoría de Morse discreta ya estudiados en el caso finito. En un principio, dicho estudio se centrará en ...
    • IconUna Introducción a la pretopología  [Final Degree Work]

      Velaure Valera, Elena (2019)
      The main goal of this Final Degree Project is the study of pretopological spaces. Being more precise, certain properties of general topology will be presented: separation axioms and the different notions of connectedness ...
    • IconLusternik-Schnirelmann category of simplicial complexes and finite spaces  [Article]

      Fernández Ternero, Desamparados; Macías Viirgós, Enrique; Vilches Alarcón, José Antonio (Elsevier, 2015-10)
      In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This simplicial category has the property of being invariant under strong ...
    • IconPerfect discrete Morse functions on 2-complexes  [Article]

      Ayala Gómez, Rafael; Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio (Universidad de Sevilla, 2010)
      This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete Morse functions such that the number of critical i-simplices coincides with the i-th Betti number ...
    • IconSobre las diferentes nociones topológicas de complejo y algunas de sus aplicaciones  [Final Degree Work]

      Núñez de Arco Valenzuela, Laura (2016-12)
      The main goal of this work is to introduce the different kinds of combinatorial structures used in topological data analysis. It is focused on a detailed description of certain types of simplicial, cubical and cellular ...
    • IconStructural aspects of the non-uniformly continuous functions and the unbounded functions within C(X)  [Article]

      Ayala Gómez, Rafael; Bernal González, Luis; Calderón Moreno, María del Carmen; Vilches Alarcón, José Antonio (Elsevier, 2019-04-01)
      We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, under appropriate mild assumptions, there exists in fact a plethora of such functions, in both ...