Applied General Topology - Vol 02, No 1 (2001)
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Research articles
- On topological sequence entropy of circle maps
- Fell type topologies of quasi-pseudo-metric spaces and the Kuratowski-Painlevé convergence
- Continuous representability of complete preorders on the space of upper-continuous capacities
- F-points in countably compact spaces
- Common fixed point theorems for a countable family of fuzzy mappings
- New results on topological dynamics of antitriangular maps
- A contribution to the study of fuzzy metric spaces
- Attractor of reaction-diffusion equations in Banach spaces
- Weak completeness of the Bourbaki quasi-uniformity
- Flows equivalences
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- PublicationCommon fixed point theorems for a countable family of fuzzy mappings(Universitat Politècnica de València, 2001-04-01) Vidal, Anna; Universitat Politècnica de València; Generalitat Valenciana[EN] In this paper we prove fixed point theorems for countable families of fuzzy mappings satisfying contractive-type conditions and a rational inequality in left K-sequentially complete quasi-pseudo-metric spaces. These results generalize the corresponding ones obtained by others authors.
- PublicationFlows equivalences(Universitat Politècnica de València, 2001-04-01) Soler López, Gabriel; Ministerio de Educación y Cultura[EN] Given a differential equation on an open set O of an n-manifold we can associate to it a pseudo-flow, that is, a flow whose trajectories may not be defined in the entire real line. In this paper we prove that this pseudo-flow is always equivalent to a flow with its trajectories defined in all R. This result extends a similar result of Vinograd stated in the n-dimensional Euclidean space.
- PublicationF-points in countably compact spaces(Universitat Politècnica de València, 2001-04-01) Bella, Angelo; Malykhin, V.I.; Ministero dell'università e della ricerca scientifica e tecnologica, Italia[EN] Answering a question of A.V. Arhangel'skii, we show that any extremally disconnected subspace of a compact space with countable tightness is discrete.
- PublicationA contribution to the study of fuzzy metric spaces(Universitat Politècnica de València, 2001-04-01) Sapena Piera, Almanzor; Dpto. de Matemática Aplicada; Escuela Politécnica Superior de Gandia; Instituto de Investigación para la Gestión Integrada de Zonas Costeras[EN] We give some examples nad properties of fuzzy metric spaces, in the sense of George and Veramani, and characterize the To topological spaces which admit a compatible uniformity that has a countable transitive base, in terms of the fuzzy theory.
- PublicationAttractor of reaction-diffusion equations in Banach spaces(Universitat Politècnica de València, 2001-04-01) Valero, José[EN] In this paper we prove first some abstract theorems on existence of global attractors for differential inclusions generated by w-dissipative operators. Then these results are applied to reaction-diffusion equations in which the Babach space Lp is used as phase space. Finally, new results concerning the fractal dimension of the global attractor in the space L2 are obtained.
- PublicationOn topological sequence entropy of circle maps(Universitat Politècnica de València, 2001-04-01) Cánovas, José S.; Ministerio de Educación y Cultura[EN] We classify completely continuous circle maps from the point of view of topological sequence entropy. This improves a result of Roman Hric.
- PublicationContinuous representability of complete preorders on the space of upper-continuous capacities(Universitat Politècnica de València, 2001-04-01) Bosi, Gianni; Isler, Romano[EN] Given a compact metric space (X, d), and its Borel σ-algebra Σ, we discuss the existence of a (semi)continuous utility function U for a complete preorder ≤ on a subset M’(X) of the space M(X) of all upper-continuous capacities on Σ, endowed with the weak topology.
- PublicationNew results on topological dynamics of antitriangular maps(Universitat Politècnica de València, 2001-04-01) Balibrea, Francisco; Cánovas, J.S.; Linero, A.; Ministerio de Educación y Cultura[EN] We present some results concerning the topological dynamics of antitriangular maps, F:X2→ X2 with the formvF(x,y)=(g(y),f(x)), where (X,d) is a compact metric space and f,g : X→ X are continuous maps. We make an special analysis in the case of X = [0,1].
- PublicationWeak completeness of the Bourbaki quasi-uniformity(Universitat Politècnica de València, 2001-04-01) Sánchez Granero, M.A.; Ministerio de Ciencia y Tecnología[EN] The concept of semicompleteness (weaker than half-completeness) is defined for the Bourbaki quasi-uniformity of the hyperspace of a quasi-uniform space. It is proved that the Bourbaki quasi-uniformity is semicomplete in the space of nonempty sets of a quasi-uniform space (X,U) if and only if each stable filter on (X,U*) has a cluster point in (X,U). As a consequence the space of nonempty sets of a quasi-pseudometric space is semicomplete if and only if the space itself is half-complete. It is also given a characterization of semicompleteness of the space of nonempty U*-compact sets of a quasi-uniform space (X,U) which extends the well known Zenor-Morita theorem.
- PublicationFell type topologies of quasi-pseudo-metric spaces and the Kuratowski-Painlevé convergence(Universitat Politècnica de València, 2001-04-01) Rodríguez-López, Jesús[EN] We study the double Fell topology when this hypertopology is constructed over a quasi-pseudo-metric space. In particular, its relationship with the Wijsman hypertopology is studied. We also propose an extension of the Kuratowski-Painlevé convergence in the bitopological setting.