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Autor Rodríguez Sanjurjo, José Manuel |
Documentos disponibles escritos por este autor (61)
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In ANR theory, the following result is well known: Suppose that X ? is an ANR and X is a subspace of X ? . Then X is a strong (or stationary) deformation retract of X ? if and only if X is a deformation retract of X ? . In this paper, a[...]![]()
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The notions of quasidomination and quasi-equivalence of compacta were introduced by K. Borsuk [Fund. Math. 93 (1976), no. 3, 197–212. These relations are weaker than the relations of shape domination and shape equivalence. According to Borsuk th[...]![]()
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Laguna, V.F. ; Morón, Manuel A. ; Rodríguez Sanjurjo, José Manuel | Symposium of General Topology | 1990S. Godlewski [Fundam. Math. 114, 1-9 (1981; Zbl 0498.54016)] proved that if a metrizable space X is a mutational retract of X0 and X is an MANR (mutational absolute neighborhood retract), then every component of X is a mutational retract of a co[...]![]()
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We study the internal structure of the global attractor of a uniformly persistent flow. We show that the restriction of the flow to the global attractor has duality properties which can be expressed in terms of certain attractor-repeller decompo[...]![]()
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K. Borsuk [Fund. Math. 99 (1978), no. 1, 35–42] extended the classical notion of Lyusternik-Shnirelman category (briefly L-S category) to the theory of shape and thereby introduced a shape invariant coefficient for a compactum X . This was subse[...]![]()
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Sánchez Gabites, Jaime Jorge ; Rodríguez Sanjurjo, José Manuel | American Mathematical Society | 2007Suppose phi : M x R -> M is a continuous flow on a locally compact metrizable space M and K is an ( asymptotically stable) attractor. Let D =partial derivative A( K) be the boundary of the basin of attraction of K. In the present paper it will [...]![]()
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The author generalizes some results of Ball concerning the relationship between the shape of a locally compact metrizable space with compact components and the shape of its components. The following results are proved. Let X and Y be locally com[...]![]()
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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[...]![]()
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Let X, Y be two compacta with Sh(X) = Sh (Y). Then, the spaces of components of X, Y are homeomorphic. This does not happen, in general, when X, Y are quasi-equivalent. In this paper we give a sufficient condition for the existence of a homeomor[...]![]()
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Given an approximate mapping f ? ={f k }:X?Y between compacta from the Hilbert cube [K. Borsuk, Fund. Math. 62 (1968), 223–254, the author associates with f ? a (u.s.c.) multivalued mapping F:X?Y . If F is single-valued, F and f ? induce [...]![]()
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This article is an exposition of several results concerning the theory of continuous dynamical systems, in which Topology plays a key role. We study homological and homotopical properties of attractors and isolated invariant compacta as well as [...]![]()
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Morón, Manuel A. ; Romero Ruiz del Portal, Francisco ; Rodríguez Sanjurjo, José Manuel | Elsevier Science | 1994-02-21We use N-compactifications of 0-dimensional spaces to obtain a new shape invariant for the class of all topological spaces. We also point out that the shape and topological classifications are not the same in the realm of Tychonov spaces having [...]![]()
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The author treats shape properties which movable compacta and their nonmovable components inherit from their movable components. First he shows that shape morphisms of movable compacta are completely determined by their restrictions to movable c[...]![]()
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An upper semicontinuous multivalued map F:X?Y is said to be ? -small if the diameter of F(x) is less than ? for each x?X . F and G are ? -homotopic if there is an ? -small homotopy H:X×I?Y joining F and G . F:X×[0,?)?Y is a fine multival[...]![]()
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For compact metric spaces X , Y contained in a given compact AR Q , the authors consider the set A(X,Y) of all approximative maps (in the sense of K. Borsuk [same journal 62 (1968), 223–254]). On A(X,Y) they define a metric making A(X,Y) a c[...]![]()
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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.![]()
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Sánchez Gabites, Jaime Jorge ; Rodríguez Sanjurjo, José Manuel | Croatian Mathematical Society; Department of Mathematics, University of Zagreb | 2007-06A compact stable attractor K of a continuous flow on a locally compact metric space is shape equivalent to a compact positively invariant neighbourhood P in its basin of attraction, the shape equivalence being induced by the inclusion map. In [...]![]()
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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; [...]![]()
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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[...]![]()
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In this paper the author studies homotopy properties of FANR spaces (fundamental absolute neighborhood retracts). The principal result is a theorem about homotopy extensions for fundamental ? -near sequences such that the initial and final level[...]![]()
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Laguna, V. F. ; Rodríguez Sanjurjo, José Manuel | Japanese Association of mathematical Sciences | 1986Let A(X,Y) be the set of all approximate maps ofa compactum X to a compactum Y. In this paper we define two topologies on A(X,Y) and study some properties of the spaces obtained.![]()
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The authors study the space $A\sp*(X,Y)$ of all approximative maps f\{f\sb k: X\to Y\}$ between compact subsets X, Y of the Hilbert cube. The topology of this space is given by the pseudometric $d\sp*(\underline f,\underline g)=\inf \{\sup \{d[...]