Data

NameAyala Gómez, Rafael
DepartmentGeometría y Topología
Knowledge areaGeometría y Topología
Professional categoryProfesor Titular de Universidad
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  Statistics

  • Items

    26

  • Visits

    1778

  • Downloads

    2887

  Publications

 

Article
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Structural aspects of the non-uniformly continuous functions and the unbounded functions within C(X)

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, ...
Final Degree Project
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Una Introducción a la pretopología

Ayala Gómez, Rafael; Vilches Alarcón, José Antonio; Velaure Valera, Elena (2019-01-01)
The main goal of this Final Degree Project is the study of pretopological spaces. Being more precise, certain properties ...
Final Degree Project
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Espacios pretopológicos: algunas aplicaciones

Ayala Gómez, Rafael; Vilches Alarcón, José Antonio; González Puntas, Gloria (2018-01-01)
The goal of this work is to study the theory of pretopological spaces and some applications. Starting with the key notion ...
Final Degree Project
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Sobre las diferentes nociones topológicas de complejo y algunas de sus aplicaciones

Ayala Gómez, Rafael; Vilches Alarcón, José Antonio; Núñez de Arco Valenzuela, Laura (2016-12-01)
The main goal of this work is to introduce the different kinds of combinatorial structures used in topological data analysis. ...
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, 2010-01-01)
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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Perfect discrete Morse functions on 2-complexes

Ayala Gómez, Rafael; Fernández Ternero, Desamparados; Vilches Alarcón, José Antonio (Universidad de Sevilla, 2010-01-01)
This paper is focused on the study of perfect discrete Morse functions on a 2-simplicial complex. These are those discrete ...
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Discrete Morse inequalities on infinite graphs

Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio; Ayala Gómez, Rafael (2009-01-01)
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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, 2008-01-01)
The aim of this paper is to study the notion of critical element of a proper discrete Morse function defined on non-compact ...
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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 ...
Presentation
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Defining discrete Morse functions on infinite surfaces

Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel (2004-01-01)
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.
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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 ...
PhD Thesis
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Funciones de Morse discretas sobre complejos infinitos

Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio (2003-01-01)
Esta memoria está dedicada a la extensión para complejos simpliciales infinitos de los conceptos y resultados de la teoría ...
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On the connectivity of skeletons of pseudomanifolds with boundary

Ayala Gómez, Rafael; Chávez de Diego, María José; Márquez Pérez, Alberto; Quintero Toscano, Antonio Rafael (Mathematical Institute, Academy of Sciences of the Czech Republic, 2002-01-01)
In this note we show that 1-skeletons and 2-skeletons of n-pseudomanifolds with full boundary are (n+ 1)-connected graphs and n-connected 2-complexes, respectively. This generalizes previous results due to Barnette and Woon.
Presentation
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Desigualdades de Morse generalizadas sobre grafos

Ayala Gómez, Rafael; Fernández Fernández, Luis Manuel; Vilches Alarcón, José Antonio (Alberto Márquez, 2002-01-01)
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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, 2001-11-01)
This paper is devoted to prove a Digital Index Theorem for digital (n − 1)-manifolds in a digital space (Rn, f), where f ...
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The equivariant category of proper G-Spaces

Ayala Gómez, Rafael; Fernández Lasheras, Francisco Jesús; Quintero Toscano, Antonio Rafael (Rocky Mountain Mathematics Consortium, 2001-01-01)
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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, 1999-01-01)
This paper contains a study of the connectivity of infinite graphs and 2-complexes. Various connectivity types are defined ...
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 (1995-01-01)
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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Moore spaces in proper homotopy

Ayala Gómez, Rafael; Domínguez, E.; Márquez Pérez, Alberto; Quintero Toscano, Antonio Rafael (University of Tsukuba, 1995-01-01)
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.
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On the Graphs which are the Edge of a Plane Tiling

Ayala Gómez, Rafael; Domínguez, E.; Márquez Pérez, Alberto; Quintero Toscano, Antonio Rafael (Mathematica Scandinavica, 1995-01-01)
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A note on the homotopical characterization of Rn

Ayala Gómez, Rafael; Quintero Toscano, Antonio Rafael (Universitat de Barcelona, 1992-01-01)
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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Lusternik-Schnirelmann invariants in proper homotopy theory

Ayala Gómez, Rafael; Domínguez Murillo, Eladio; Márquez Pérez, Alberto; Quintero Toscano, Antonio Rafael (University of California, 1992-01-01)
We introduce and study proper homotopy invariants of the Lusternik-Schnirelmann type, p-cat (-), p-Cat(-), and cat e(-) ...
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Proper Homotopy Classification of Graphs

Ayala Gómez, Rafael; Domínguez, E.; Márquez Pérez, Alberto; Quintero Toscano, Antonio Rafael (London Mathematical Society, 1990-01-01)
This work presents a classification of the proper homotopy types of locally finite 1-dimensional CW-complexes.
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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, 1989-01-01)
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.
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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, 1988-01-01)
The purpose of this note is to prove the exponential law for uniformly continuous proper maps.
PhD Thesis
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Aproximación axiomática a las teorías de cobordismo

Domínguez Murillo, Eladio; Ayala Gómez, Rafael (1982-01-01)