Author profile: Ayala Gómez, Rafael
Institutional data
Name | Ayala Gómez, Rafael |
Department | Geometría y Topología |
Knowledge area | Geometría y Topología |
Professional category | Profesor Titular de Universidad |
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Statistics
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No. publications
32
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No. visits
4011
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No. downloads
8934
Publications |
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Final Degree Project
Convergencia de sucesiones en espacios topológicos
(2023)
En este trabajo, se trata el problema del papel de las sucesiones en los espacios topol´ogicos, desde dos puntos de vista. ... |
Final Degree Project
Topologías en el plano digital
(2022)
In this work we present the basic properties of the Khalimsky topology on Z 2 . This topology is compared with the Marcus-Wyse ... |
Final Degree Project
Espacios de Convergencia
(2022)
The main goal of this proyect is to deepen in the study of the Convergence Spaces which are a generalization of the ... |
Final Degree Project
Algunos aspectos de la teoría de (ultra)filtros
(2022)
The notions of filter and ultrafilter are introduced in the field of General Topology to extend the notion of convergence ... |
Final Degree Project
Espacios de clausura de Čech
(2021)
Čech closure spaces were defined by Čech in [3] and are obtained from Kuratowsky closure operator by omitting the idempotent ... |
Article
Structural aspects of the non-uniformly continuous functions and the unbounded functions within C(X)
(Elsevier, 2019)
We prove in this paper that if a metric space supports a real continuous function which is not uniformly continuous then, ... |
Final Degree Project
Una Introducción a la pretopología
(2019)
The main goal of this Final Degree Project is the study of pretopological spaces. Being more precise, certain properties ... |
Final Degree Project
Espacios pretopológicos: algunas aplicaciones
(2018)
The goal of this work is to study the theory of pretopological spaces and some applications. Starting with the key notion ... |
Final Degree Project
Sobre las diferentes nociones topológicas de complejo y algunas de sus aplicaciones
(2016)
The main goal of this work is to introduce the different kinds of combinatorial structures used in topological data analysis. ... |
Article
Counting excellent discrete Morse functions on compact orientable surfaces
(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. |
Article
Perfect discrete Morse functions on 2-complexes
(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 ... |
Article |
Article
Critical elements of proper discrete Morse functions
(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 ... |
Article
Digital homotopy with obstacles
(Elsevier, 2004)
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
Defining discrete Morse functions on infinite surfaces
(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. |
Article
Homotopy in digital spaces
(Elsevier, 2003)
The main contribution of this paper is a new “extrinsic” digital fundamental group that can be readily generalized to ... |
PhD Thesis
Funciones de Morse discretas sobre complejos infinitos
(2003)
Esta memoria está dedicada a la extensión para complejos simpliciales infinitos de los conceptos y resultados de la teoría ... |
Presentation
Desigualdades de Morse generalizadas sobre grafos
(Alberto Márquez, 2002)
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Article
On the connectivity of skeletons of pseudomanifolds with boundary
(Mathematical Institute, Academy of Sciences of the Czech Republic, 2002)
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. |
Article
A digital index theorem
(World Scientific Publishing, 2001)
This paper is devoted to prove a Digital Index Theorem for digital (n − 1)-manifolds in a digital space (Rn, f), where f ... |
Article
The equivariant category of proper G-Spaces
(Rocky Mountain Mathematics Consortium, 2001)
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Article
On the connectivity of infinite graphs and 2-complexes
(Elsevier, 1999)
This paper contains a study of the connectivity of infinite graphs and 2-complexes. Various connectivity types are defined ... |
Article
On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor
(Institute of Mathematics, Polish Academy of Sciences, 1998)
We extend a theorem of S. Claytor in order to characterize the Peano generalized continua which are embeddable into the ... |
Presentation
On surfaces in digital topology
(1995)
In R. Ayala, E. Domínguez, A.R. Francés, A. Quintero, J. Rubio. A Polyhedral Approach to Digital Topology a new framework ... |
Article
Moore spaces in proper homotopy
(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. |
Article
On the Graphs which are the Edge of a Plane Tiling
(Mathematica Scandinavica, 1995)
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Article
Lusternik-Schnirelmann invariants in proper homotopy theory
(University of California, 1992)
We introduce and study proper homotopy invariants of the Lusternik-Schnirelmann type, p-cat (-), p-Cat(-), and cat e(-) ... |
Article
A note on the homotopical characterization of Rn
(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. |
Article
Proper Homotopy Classification of Graphs
(London Mathematical Society, 1990)
This work presents a classification of the proper homotopy types of locally finite 1-dimensional CW-complexes. |
Article
Approximation axiomatique à la théorie du bordisme
(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. |
Article
Exponential law for uniformly continous proper maps
(Universitat Autònoma de Barcelona, 1988)
The purpose of this note is to prove the exponential law for uniformly continuous proper maps. |
PhD Thesis |