Person: Rodríguez Sanjurjo, José Manuel
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First Name
José Manuel
Last Name
Rodríguez Sanjurjo
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Álgebra, Geometría y Topología
Area
Geometría y Topología
Identifiers
65 results
Search Results
Now showing 1 - 10 of 65
Item On limits of shape maps(Topology and its Applications, 1986) Rodríguez Sanjurjo, José ManuelThe notions of accessible and strongly accessible approximative maps are defined and studied. Approximative maps obtained as limits of sequences of shape equivalences are strongly accessible. It is proved that strongly accessible approximative maps induce pseudo-isomorphisms in the sense of H. Kato. It is also seen that, under the assumption of calmness, shape morphisms induced by accessible approximative maps are left invertible. As an application some results of L. Boxer concerning approximately invertible maps are generalized.Item Generalized refinable maps and images of FANR's(Topology and its Applications, 1991) Fernández Laguna, Víctor; Alonso Morón, Manuel; Rodríguez Sanjurjo, José ManuelIn 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 characterise those weakly refinable maps which preserve FANR's and using a result of Boxer we characterise the weakly refinable maps which preserve ANR's.Item Multifibrations. A class of shape fibrations with the path lifting property(Czechoslovak Mathematical Journal, 2001) Giraldo, A.; Rodríguez Sanjurjo, José ManuelIn 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. Multifibrations have the interesting property of being characterized in a completely intrinsic. way by a path lifting property involving only the total and the base space of the fibration. We also show that multifibrations land also, with some restrictions, shape fibrations) have a lifting property for homotopies of fine multivalued maps. This implies, when the spaces considered are metric compacta, that the possibility of lifting a fine multivalued map is a property of the corresponding strong shape morphism and not of the particular map considered.Item Algunas propiedades de los compactos movibles.(Publicacions Matemàtiques, 1980) Rodríguez Sanjurjo, José ManuelSome 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.Item Movability and limits of polyhedra(Fundamenta Mathematicae, 1993) Fernández Laguna, Víctor; Alonso Morón, Manuel; Nhu, Nguyen Tho; Rodríguez Sanjurjo, José ManuelWe 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 polyhedra in the shape metric. This fact is applied to show that the hyperspace (2R2, d(S)) is separable. On the other hand, we give an example showing that 2R2 is not separable in the fundamental metric introduced by Borsuk.Item On the global structure of invariant regions of flows with asymptotically stable attractors(Mathematische Zeitschrift, 1999) Giraldo, A.; Rodríguez Sanjurjo, José ManuelItem A topology for the sets of shape morphisms(Topology and its Applications, 1999) Cuchillo Ibáñez, Eduardo; Alonso Morón, Manuel; Romero Ruiz Del Portal, Francisco; Rodríguez Sanjurjo, José ManuelWe introduce a topology on the set of shape morphisms between arbitrary topological spaces X, Y, Sh(X, Y). These spaces allow us to extend, in a natural way, some classical concepts to the realm of topological spaces. Several applications are given to obtain relations between shape theory and N-compactness and shape-theoretic properties of the spaces of quasicomponents.Item The topology of dissipative systems(2023) Rodríguez Sanjurjo, José Manuel; Barge, Héctor; Sanjurjo Rodríguez, José ManuelThis expository article is dedicated to the study of some topological features of dissipative flows defined in locally compact metric spaces, especially in manifolds and in the Euclidean space. We show that they exhibit a host of interesting topological properties in areas as diverse as Conley’s index theory, population dynamics, and the dynamics of planar systems.Item Multihomotopy, Čech Spaces of loops and Shape Groups(Proceedings of the London Mathematical Society, 1994) Rodríguez Sanjurjo, José ManuelRecently, 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, whose values Fk(x), x∈X, have diameters tending to 0. Shape morphisms X→Y are defined as homotopy classes of multi-nets [J. M. R. Sanjurjo, Trans. Amer. Math. Soc. 329 (1992), no. 2, 625–636. In the present paper the author considers the set N(X,Y) of all multi-nets and endows it with a T0-topology. It is proved that two multi-nets are homotopic if and only if they belong to the same path-component of N(X,Y). A certain subspace of N(I,X), I=[0,1], is the Čech space of loops Ωˇ(X,x0). Its path components can be identified with the first shape group πˇ1(X,x0). The author also shows that the nth shape group πˇn(X,x0) coincides with a certain subgroup of the fundamental group of the iterated loop space Ωˇn−1(X,x0). These results assume a simple form if they are applied to internally movable compacta [J. Dydak, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 1, 107–110 and internal FANRs [V. F. Laguna and J. M. R. Sanjurjo, Topology Appl. 17 (1984), no. 2, 189–197. Finally, the author considers continuous flows π:M×R→M, where M is a locally compact ANR. It is proved that every asymptotically stable compact set X⊆M is shape dominated by a compact polyhedron, i.e., X is an FANR. In a remark the author points out that this theorem has also been obtained independently by B. Günther and J. Segal [Proc. Amer. Math. Soc. 119 (1993), no. 1, 321–329.Item Shape morphisms and spaces of approximative maps(Fundamenta Mathematicae, 1989) Laguna, V. F.; Rodríguez Sanjurjo, José ManuelFor 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 connected separable metric space, which contains the space of continuous mappings Y X as a closed subset. Moreover, path components of A(X,Y) coincide with homotopy classes of approximative maps. The latter property is of interest in view of the fact that these classes can be interpreted as shape morphisms from X to Y . Previously defined metrics on A(X,Y) had only the property that path connected approximative maps were homotopic, but the converse did not hold [the authors, Math. Japon. 31 (1986), no. 4, 623–633].