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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.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
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[...]texto impreso
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[...]texto impreso
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Romero Ruiz del Portal, Francisco ; Giraldo, A. ; Jimenez, R. ; Morón, Manuel A. ; Rodríguez Sanjurjo, José Manuel | Elsevier | 2011In this paper we consider two notions of attractors for semidynamical systems de ned in metric spaces. We show that Borsuk's weak and strong shape theories are a convenient framework to study the global properties which the attractor inherits fr[...]texto impreso
Giraldo, A. ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco ; Rodríguez Sanjurjo, José Manuel | Pergamon-Elsevier Science | 2005-02In this paper, we apply the notion and properties of compactly generated shape to study attractors in topological spaces.texto impreso
Giraldo, A. ; Rodríguez Sanjurjo, José Manuel | Society for Industrial and Applied Mathematics | 2009We study dynamical and topological properties of the singularities of continuations of attractors of flows on manifolds. Despite the fact that these singularities are not isolated invariant sets, they share many of the properties of attractors; [...]texto impreso
Giraldo, A. ; Morón, Manuel A. ; Romero Ruiz del Portal, Francisco ; Rodríguez Sanjurjo, José Manuel | Elsevier Science | 2001-06-29We show in this paper that the class of compacts that call be isolated non-saddle sets of flows in ANRs is precisely the class of compacta with polyhedral shape. We also prove-reinforcing the essential role played by shape theory in this setting[...]texto impreso
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This paper is devoted to introducing additional structure on ?ech homology groups. First, we redefine the ?ech homology groups in terms of what we have called approximative homology by using approximative sequences of cycles, just as Borsuk intr[...]texto impreso
We consider parameterized families of flows in locally compact metrizable spaces and give a characterization of those parameterized families of flows for which uniform persistence continues. On the other hand, we study the generalized Poincare-A[...]
