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Autor Rodríguez Sanjurjo, José Manuel |
Documentos disponibles escritos por este autor (61)
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Some properties of movable compacta are given in aonnection with quasi-dominación and likeness. The main result is the following : Let X,Y be two comnacta. If Y is movable and X-like then Y is quasi-dominated by X.![]()
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We give in this paper a description of the shape category of compacta in terms of multivalued maps. We introduce the notion of a multi-net and prove that the shape category of compacta is isomorphic to the category HN whose objects are metric co[...]![]()
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Some extension properties of maps defined on dense subsets are studied for approximate polyhedra. The latter are characterised as approximate extensors for finite maps with small oscillation.![]()
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The aim of this paper is to present a brief survey of some aspects of the theory of approximative retracts. We put special emphasis on properties of approximative absolute neighborhood retracts (both in the sense of Noguchi and in the sense of C[...]![]()
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This paper is devoted to the study of some aspects of the stability theory of flows. In particular, we study Morse decompositions induced by non-saddle sets, including their corresponding Morse equations, attractor-repeller splittings of non-sad[...]![]()
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We show in this paper that the category of shape can be modelled in discrete terms using maps defined in dense subsets of compacta. This approach to shape provides in addition a characterization of the shape of compacta which does not require ex[...]![]()
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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[...]![]()
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We define a semidynamical system - inspired by some classical dynamical systems studied by Bebutov in function spaces - in the space of approximative maps A(X, Y) between two metric compacta, with a suitable metric. Shape and strong shape morphi[...]![]()
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Fernández Laguna, Víctor ; Morón, Manuel A. ; Rodríguez Sanjurjo, José Manuel | Elsevier Science | 1991-07-31In this paper we study certain shape and homotopy properties of refinable and weakly refinable maps. In particular we give a sufficient condition for a weakly refinable map to be a homotopy domination when the codomain is an ANR. We also charact[...]![]()
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Rodríguez Sanjurjo, José Manuel ; Ruiz Sancho, Jesús María | Addison-Wesley Iberoamericana España | 1998Este libro presenta, de modo directo y accesible, las nociones y los resultados básicos de la geometría proyectiva: variedades y aplicaciones proyectivas, razón doble, homografías y cuádricas. La exposición teórica se completa con notas históric[...]![]()
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We study the homotopical and homological properties of the attractors evolving from a generalized Hopf bifurcation. We consider the Lorenz equations for parameter values near the Hopf bifurcation and study a natural Morse decomposition of the gl[...]![]()
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We introduce the notion of internal fundamental sequence and prove that any shape morphism from an arbitrary compactum X to an internally movable compactum Y is induced by an internal fundamental sequence. We use this special kind of fundamental[...]![]()
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We study in this paper some properties of the Lusternik-Schnirelmann category of isolated invariant sets of continuous dynamical systems. There are several different definitions of this coefficient, although most of them agree in the important c[...]![]()
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We establish an inequality relating the Lusternik-Schnirelmann coefficient of the unstable manifold of an isolated invariant set of a flow and the coefficients of a Morse decomposition of this set. We also establish some homological relations be[...]![]()
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Castrillón López, Marco ; Martín Peinador, Elena ; Rodríguez Sanjurjo, José Manuel ; Ruiz Sancho, Jesús María | Departamento de Geometría y Topología | 2015-09This volume contains the contributions presented by several colleagues as a tribute to the mathematical and human qualities of José María Montesinos Amilibia on the occasion of his seventieth birthday. The editors would like to express their tha[...]![]()
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We describe a new way of obtaining the Morse equations of a Morse decomposition of an isolated invariant set. This is achieved through a filtration of truncated unstable manifolds associated with the decomposition. The results in the paper make [...]![]()
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The notion of a non-saddle decomposition of a compact ANR is introduced. This notion extends that of a an attractor-repeller pair. Some cohomological properties of non-saddle decompositions are studied. In particular, some inequalities in the sp[...]![]()
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Fernández Laguna, Víctor ; Morón, Manuel A. ; Nhu, Nguyen Tho ; Rodríguez Sanjurjo, José Manuel | Polish acad sciences inst mathematics | 1993We define a metric d(S), called the shape metric, on the hyperspace 2X of all non-empty compact subsets of a metric space X. Using it we prove that a compactum X in the Hilbert cube is movable if and only if X is the limit of a sequence of polyh[...]![]()
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Giraldo, A. ; Rodríguez Sanjurjo, José Manuel | Mathematical Institute of the Academy of Sciences of the Czech Republic | 2001In this paper we introduce a class of maps possessing a multivalued homotopy lifting property with respect to every topological space. We call these maps multifibrations and they represent a formally stronger concept than that of shape fibration[...]![]()
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Recently, the author has given an alternate (and intrinsic) description of the shape category of metric compacta, based on the notion of multi-nets F:X?Y. These are defined as sequences (Fk) of upper semicontinuous multivalued mappings Fk:X?Y, w[...]![]()
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Under suitable hypotheses the well known notion of first prolongational set J(+) gives rise to a multivalued map Psi : X -> 2(X) which is continuous when the upper semifinite topology is considered in the hyperspace of X. Some important dynamic[...]![]()
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Given two shape morphisms F,G:X?Y , where X and Y are compacta, one declares F to be a divisor of G provided for any compactum Z and any shape morphism U:X?Z if F factors as F=F 1 ?U , then G factors as G=G 1 ?U . On the other hand, if S[...]![]()
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The author introduces the notion of an ? -fundamental retraction which combines conditions that are used in Borsuk's shape theory, the reviewer's approximate shape theory, and Bogatyi's internal shape theory. This concept is used to define a cla[...]