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Hernández Corbato, Luis ; Le Calvez , Patrice ; Romero Ruiz del Portal, Francisco | Geometry & Topology Publications, Univ Warwick, Mathematics Inst | 2013This article includes an almost self-contained exposition on the discrete Conley index and its duality. We work with a locally defined homeomorphism f in R-d and an acyclic continuum X, such as a cellular set or a fixed point, invariant under f [...]texto impreso
Cuchillo Ibáñez, Eduardo ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco | Editorial Complutense | 1994This interesting and well-written survey article is devoted to the class P of topological spaces in which components and quasi-components coincide. This class includes the compact Hausdorff spaces and the locally connected spaces. It also inclu[...]texto impreso
Carabantes Alarcón, David ; Ancochea Soto, Eumenio ; Arias Astray, Andrés ; Dupont Sfez, Samuelle ; Iglesias Recuero, Silvia ; Manjón-Cabeza Olmeda, Araceli ; Martín Martín, José Oliver ; Montero de Juan, Francisco Javier ; Romero Ruiz del Portal, Francisco ; San Andrés Moya, Margarita ; Sastre Castillo, Miguel Ángel ; Tirado Fernández, Francisco | 2018-06-30El Aprendizaje Servicio es una estrategia docente necesaria para el desarrollo de iniciativas de emprendimiento e innovación social, que partan desde la Universidad, y que se puedan incorporar en las diferentes áreas de conocimiento de la UCMtexto impreso
Hernández Corbato, Luis ; Ortega, Rafael ; Romero Ruiz del Portal, Francisco | Cambridge Univ Press | 2012Let h : R-2 -> R-2 be a dissipative and orientation preserving homeomorphism having an asymptotically stable fixed point. Let U be the region of attraction and assume that it is proper and unbounded. Using Caratheodory's prime ends theory one c[...]texto impreso
Given an orientation-preserving homeomorphism of the plane, a rotation number can be associated with each locally attracting fixed point. Assuming that the homeomorphism is dissipative and the rotation number vanishes we prove the existence of a[...]texto impreso
A bimorphism is both an epimorphism and a monomorphism. If every bimorphism is an iso then the given category is said to be balanced. Such notions are studied in several contexts (pro-categories, pro-homotopy, shape, proper homotopy). The refere[...]texto impreso
The authors deal with the question of whether the sets of shape and homotopy types of FANRs are countable. FANRs can be considered as a natural generalization of ANRs; thus the authors' starting point consists of results on the countability of t[...]texto impreso
Giraldo, A. ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco ; Rodríguez Sanjurjo, José Manuel | Elsevier Science B.V. (North-Holland) | 2001-09-07We show in this paper how to represent intrinsically Cech homology of compacta, in terms of inverse limits of discrete approximations. We establish some relations between inverse limits and non-continuous homotopies and, as a consequence, we get[...]texto impreso
The author proves that if f is an orientation reversing homeomorphism of the plane and p is an isolated and stable fixed point of f then the fixed point index of f at p is equal to 1 . In the orientation preserving case this result was obta[...]texto impreso
Let U c R2 be an open subset and let f :U ? f (U) c R2 be a homeomorphism. Let M = M1 U· · ·U Mr C U be a disjoint union of discs that isolates the invariant compactum K. The aimof this paper is to study the dynamics of f in K and to use the fix[...]texto impreso
Let X be a locally compact metric absolute neighbourhood retract for metric spaces, U subset of X be an open subset and f:U --> X be a continuous map. The aim of the paper is to study the fixed point index of the map that f induces in the hypers[...]texto impreso
Let X be a locally compact metric absolute neighbourhood retract for metric spaces, U?X be an open subset and f :U?X be a continuous map. The aim of the paper is to study the fixed point index of the map that f induces in the y perspace of X. Fo[...]texto impreso
Let U be an open subset of R2 and let f :U ? R2 be a local homeomorphism. Let p € U be a non-repeller 4xed point of f suchth at {p} is an isolated invariant set. We introduce a particular class of index pairs for {p} that we call generalized 4lt[...]texto impreso
Hernández Corbato, Luis ; Romero Ruiz del Portal, Francisco | American Institute of Mathematical Sciences | 2015-07We characterize the sequences of fixed point indices {i(f(n) ,p)} n > = 1 of fixed points that are isolated as an invariant set for a continuous map f in the plane. In particular, we prove that the sequence is periodic and i(f(n) ,p) = 0. This[...]texto impreso
In this paper we apply the generalized degree introduced by Geba, Massabo and Vignoli, in [3], to extend the notion of complementing maps defined by Fitzpatrick, Massabo and Pejsachowicz, in [1] and [2]. On the other hand, we obtain, in low dime[...]
