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Autor Rodríguez Sanjurjo, José Manuel |
Documentos disponibles escritos por este autor (61)
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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[...]![]()
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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[...]