Now showing items 1-20 of 27

    • Article
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      A digital index theorem 

      Domínguez Murillo, Eladio; Francés Román, Ángel Ramón; Ayala Gómez, Rafael; Quintero Toscano, Antonio Rafael (World Scientific Publishing, 2001-11)
      This paper is devoted to prove a Digital Index Theorem for digital (n − 1)-manifolds in a digital space (Rn, f), where f ...
    • Article
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      A note on the homotopical characterization of Rn 

      Ayala Gómez, Rafael; Quintero Toscano, Antonio Rafael (Universitat de Barcelona, 1992)
      This note gives conditions which assure that the one-point compactification of an open manifold is a manifold. This result is used to show that the homotopical characterization of Rn (n ≥ 4) can be derived from the Poincaré Conjecture.
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      Approximation axiomatique à la théorie du bordisme 

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Quintero Toscano, Antonio Rafael (Université de Picardie Jules Verne, 1989)
      This paper gives an axiomatical approximation to Bordism Theory. It proves those properties of a geometrical nature that a class of models must satisfy to develop a bordism theory in an abstract category.
    • PhD Thesis
    • Article
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      Counting excellent discrete Morse functions on compact orientable surfaces 

      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.
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      Critical elements of proper discrete Morse functions 

      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 ...
    • Presentation
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      Defining discrete Morse functions on infinite surfaces 

      Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel (2004)
      We present an algorithm which defines a discrete Morse function in Forman’s sense on an infinite surface including a study of the minimality of this function.
    • Presentation
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      Desigualdades de Morse generalizadas sobre grafos 

      Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio (Alberto Márquez, 2002)
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      Digital homotopy with obstacles 

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Francés Román, Ángel Ramón; Quintero Toscano, Antonio Rafael (Elsevier, 2004-04-30)
      As a sequel of [4] Ayala, R., E. Dom´ıguez, A. R. Franc´es and A. Quintero, Homotopy in Digital Spaces, Discrete and Applied ...
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      Discrete Morse inequalities on infinite graphs 

      Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio; Ayala Gómez, Rafael (2009)
    • Final Degree Project
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      Espacios de clausura de Čech 

      Rodríguez Gómez, Manuel (2021)
      Čech closure spaces were defined by Čech in [3] and are obtained from Kuratowsky closure operator by omitting the idempotent ...
    • Final Degree Project
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      Espacios pretopológicos: algunas aplicaciones 

      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 ...
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      Exponential law for uniformly continous proper maps 

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Quintero Toscano, Antonio Rafael (Universitat Autònoma de Barcelona, 1988)
      The purpose of this note is to prove the exponential law for uniformly continuous proper maps.
    • PhD Thesis
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      Funciones de Morse discretas sobre complejos infinitos 

      Vilches Alarcón, José Antonio (2003)
      Esta memoria está dedicada a la extensión para complejos simpliciales infinitos de los conceptos y resultados de la teoría ...
    • Article
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      Homotopy in digital spaces 

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Francés Román, Ángel Ramón; Quintero Toscano, Antonio Rafael (Elsevier, 2003-01-15)
      The main contribution of this paper is a new “extrinsic” digital fundamental group that can be readily generalized to ...
    • Final Degree Project
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      Una Introducción a la pretopología 

      Velaure Valera, Elena (2019)
      The main goal of this Final Degree Project is the study of pretopological spaces. Being more precise, certain properties ...
    • Article
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      Lusternik-Schnirelmann invariants in proper homotopy theory 

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Márquez Pérez, Alberto; Quintero Toscano, Antonio Rafael (University of California, 1992)
      We introduce and study proper homotopy invariants of the Lusternik-Schnirelmann type, p-cat (-), p-Cat(-), and cat e(-) ...
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      Moore spaces in proper homotopy 

      Ayala Gómez, Rafael; Domínguez, E.; Márquez Pérez, Alberto; Quintero Toscano, Antonio Rafael (University of Tsukuba, 1995)
      Moore spaces are de ned in proper homotopy theory. Some results on the existence and uniqueness of those spaces are proven. An example of two non properly equivalent Moore spaces is given.
    • Presentation
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      On surfaces in digital topology 

      Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Francés Román, Ángel Ramón; Quintero Toscano, Antonio Rafael; Rubio Sender, Julio (1995)
      In R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, J. Rubio. A Polyhedral Approach to Digital Topology a new framework ...
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      On the connectivity of infinite graphs and 2-complexes 

      Ayala Gómez, Rafael; Chávez de Diego, María José; Márquez Pérez, Alberto; Quintero Toscano, Antonio Rafael (Elsevier, 1999)
      This paper contains a study of the connectivity of infinite graphs and 2-complexes. Various connectivity types are defined ...