Listar por autor "Ayala Gómez, Rafael"
Mostrando ítems 1-20 de 31
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Artículo
A digital index theorem
(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 ...
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Artículo
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.
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Trabajo Fin de Grado
Algunos aspectos de la teoría de (ultra)filtros
(2022-06-03)The notions of filter and ultrafilter are introduced in the field of General Topology to extend the notion of convergence ...
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Artículo
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.
- Tesis Doctoral
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Trabajo Fin de Grado
Convergencia de sucesiones en espacios topológicos
(2023-07)En este trabajo, se trata el problema del papel de las sucesiones en los espacios topol´ogicos, desde dos puntos de vista. ...
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Artículo
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.
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Artículo
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 ...
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Ponencia
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.
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Ponencia
Desigualdades de Morse generalizadas sobre grafos
(Alberto Márquez, 2002) -
Artículo
Digital homotopy with obstacles
(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 ...
- Artículo
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Trabajo Fin de Grado
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 ...
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Trabajo Fin de Grado
Espacios de Convergencia
(2022-06-22)The main goal of this proyect is to deepen in the study of the Convergence Spaces which are a generalization of the ...
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Trabajo Fin de Grado
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 ...
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Artículo
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.
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Tesis Doctoral
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 ...
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Artículo
Homotopy in digital spaces
(Elsevier, 2003-01-15)The main contribution of this paper is a new “extrinsic” digital fundamental group that can be readily generalized to ...
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Trabajo Fin de Grado
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 ...
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Artículo
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(-) ...