Applied General Topology - Vol 19, No 1 (2018)
Tabla de contenidos
- Partially topological group action
- Topological n-cells and Hilbert cubes in inverse limits
- Alternate product adjacencies in digital topology
- Set-open topologies on function spaces
- Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions
- Counting coarse subsets of a countable group
- Controlled shadowing property
- Some categorical aspects of the inverse limits in ditopological context
- Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence
- k-semistratifiable spaces and expansions of set-valued mappings
- Few remarks on maximal pseudocompactness
- Fixed point theorems for nonlinear contractions with applications to iterated function systems
- Some aspects of Isbell-convex quasi-metric spaces
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Item type: Artículo , Access status: Abierto , Some aspects of Isbell-convex quasi-metric spaces(Universitat Politècnica de València, 2018-04-02) Olela Otafudu, Olivier; National Research Foundation, South Africa; University of the Witwatersrand, Johannesburg[EN] We introduce and investigate the concept of geodesic bicombing in T0-quasi-metric spaces. We prove that any Isbell-convex T0-quasi-metric space admits a geodesic bicombing which satisfies the equivariance property. Additionally, we show that many results on geodesic bicombing hold in quasi-metric settings, provided that non symmetry in quasi-metric spaces holds.Item type: Artículo , Access status: Abierto , Fixed point theorems for nonlinear contractions with applications to iterated function systems(Universitat Politècnica de València, 2018-04-02) Pant, Rajendra[EN] We introduce a new type of nonlinear contraction and present some fixed point results without using continuity or semi-continuity. Our result complement, extend and generalize a number of fixed point theorems including the the well-known Boyd and Wong theorem [On nonlinear contractions, Proc. Amer. Math. Soc. 20(1969)]. Also we discuss an application to iterated function systems.Item type: Artículo , Access status: Abierto , Few remarks on maximal pseudocompactness(Universitat Politècnica de València, 2018-04-02) Bella, Angelo; Istituto Nazionale di Alta Matematica "F. Severi", Italia[EN] A pseudocompact space is maximal pseudocompact if every strictly finer topology is no longer pseudocompact. The main result here is a counterexample which answers a question rised by Alas, Sanchis and Wilson.Item type: Artículo , Access status: Abierto , k-semistratifiable spaces and expansions of set-valued mappings(Universitat Politècnica de València, 2018-04-02) Yan, Peng-Fei; Hu, Xing-Yu; Xie, Li-Hong[EN] In this paper, the concept of k-upper semi-continuous set-valued mappings is introduced. Using this concept, we give characterizations of k-semistratifiable and k-MCM spaces, which answers a question posed by Xie and Yan.Item type: Artículo , Access status: Abierto , Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence(Universitat Politècnica de València, 2018-04-02) Jäger, Gunther; Ahsanullah, T. M. G.[EN] We identify two categories of quantale-valued convergence tower spaces that are isomorphic to the categories of quantale-valued metric spaces and quantale-valued partial metric spaces, respectively. As an application we state a quantale-valued metrization theorem for quantale-valued convergence tower groups.Item type: Artículo , Access status: Abierto , Some categorical aspects of the inverse limits in ditopological context(Universitat Politècnica de València, 2018-04-02) Yildiz, Filiz[EN] This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category ifPDitop, whose objects are ditopological plain texture spaces and morphisms are bicontinuous point functions satisfying a compatibility condition between those spaces. In this context, the category InvifPDitop consisting of the inverse systems constructed by the objects and morphisms of ifPDitop, besides the inverse systems of mappings, described between inverse systems, is introduced, and the related ideas are studied in a categorical - functorial setting. In conclusion, an identity natural transformation is obtained in the context of inverse systems - limits constructed in ifPDitop and the ditopological infinite products are characterized by the finite products via inverse limits.Item type: Artículo , Access status: Abierto , Controlled shadowing property(Universitat Politècnica de València, 2018-04-02) Zamani Bahabadi, Alireza[EN] In this paper we introduce a new notion, named controlled shadowing property and we relate it to some notions in dynamical systems such as topological ergodicity, topologically mixing and specication properties. The relation between the controlled shadowing and chaos in sense of Li-Yorke is studied. At the end we give some examples to investigate the controlled shadowing property.Item type: Artículo , Access status: Abierto , Counting coarse subsets of a countable group(Universitat Politècnica de València, 2018-04-02) Protasov, Igor; Protasova, Ksenia[EN] For every countable group G, there are 2ω distinct classes of coarselyequivalent subsets of G.Item type: Artículo , Access status: Abierto , Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions(Universitat Politècnica de València, 2018-04-02) Ahmadullah, Md; Imdad, Mohammad; Arif, Mohammad[EN] In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those are contained in Berzig [J. Fixed Point Theory Appl. 12, 221-238 (2012))] and Alam and Imdad [To appear in Filomat (arXiv:1603.09159 (2016))]. Interestingly, a corollary to one of our main results under symmetric closure of a binary relation remains a sharpened version of a theorem due to Berzig. Finally, we use examples to highlight the accomplished improvements in the results of this paper.Item type: Artículo , Access status: Abierto , Set-open topologies on function spaces(Universitat Politècnica de València, 2018-04-02) Alqurashi, Wafa Khalaf; Khan, Liaqat Ali; Osipov, Alexander V.[EN] Let X and Y be topological spaces, F(X,Y) the set of all functions from X into Y and C(X,Y) the set of all continuous functions in F(X,Y). We study various set-open topologies tλ (λ ⊆ P(X)) on F(X,Y) and consider their existence, comparison and coincidence in the setting of Y a general topological space as well as for Y = R. Further, we consider the parallel notion of quasi-uniform convergence topologies Uλ (λ ⊆ P(X)) on F(X,Y) to discuss Uλ-closedness and right Uλ-K-completeness properties of a certain subspace of F(X,Y) in the case of Y a locally symmetric quasi-uniform space. We include some counter-examples to justify our comments.Item type: Artículo , Access status: Abierto , Alternate product adjacencies in digital topology(Universitat Politècnica de València, 2018-04-02) Boxer, Laurence[EN] We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.Item type: Artículo , Access status: Abierto , Topological n-cells and Hilbert cubes in inverse limits(Universitat Politècnica de València, 2018-04-02) Rubin, Leonard R.[EN] It has been shown by S. Mardešić that if a compact metrizable space X has dim X ≥ 1 and X is the inverse limit of an inverse sequence of compact triangulated polyhedra with simplicial bonding maps, then X must contain an arc. We are going to prove that if X = (|Ka|,pba,(A,))is an inverse system in set theory of triangulated polyhedra|Ka|with simplicial bonding functions pba and X = lim X, then there exists a uniquely determined sub-inverse system XX= (|La|, pba|Lb|,(A,)) of X where for each a, La is a subcomplex of Ka, each pba|Lb|:|Lb| → |La| is surjective, and lim XX = X. We shall use this to generalize the Mardešić result by characterizing when the inverse limit of an inverse sequence of triangulated polyhedra with simplicial bonding maps must contain a topological n-cell and do the same in the case of an inverse system of finite triangulated polyhedra with simplicial bonding maps. We shall also characterize when the inverse limit of an inverse sequence of triangulated polyhedra with simplicial bonding maps must contain an embedded copy of the Hilbert cube. In each of the above settings, all the polyhedra have the weak topology or all have the metric topology(these topologies being identical when the polyhedra are finite).Item type: Artículo , Access status: Abierto , Partially topological group action(Universitat Politècnica de València, 2018-04-02) Al Shumrani, M. A.[EN] The concept of partially topological group was recently introduced in [3]. In this article, we define partially topological group action on partially topological space and we generalize some fundamental results from topological group action theory.