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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.texto impreso
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[...]texto impreso
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.texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]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
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]texto impreso
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[...]
