Applied General Topology - Vol 19, No 1 (2018)
https://riunet.upv.es:443/handle/10251/100218
2019-07-19T00:05:45ZSome aspects of Isbell-convex quasi-metric spaces
https://riunet.upv.es:443/handle/10251/100266
Some aspects of Isbell-convex quasi-metric spaces
Olela Otafudu, Olivier
[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.
2018-04-12T06:28:56ZFixed point theorems for nonlinear contractions with applications to iterated function systems
https://riunet.upv.es:443/handle/10251/100265
Fixed point theorems for nonlinear contractions with applications to iterated function systems
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.
2018-04-12T06:20:55ZFew remarks on maximal pseudocompactness
https://riunet.upv.es:443/handle/10251/100264
Few remarks on maximal pseudocompactness
Bella, Angelo
[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.
2018-04-12T06:16:05Zk-semistratifiable spaces and expansions of set-valued mappings
https://riunet.upv.es:443/handle/10251/100263
k-semistratifiable spaces and expansions of set-valued mappings
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.
2018-04-12T06:11:50ZCharacterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence
https://riunet.upv.es:443/handle/10251/100262
Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence
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.
2018-04-12T06:05:00ZSome categorical aspects of the inverse limits in ditopological context
https://riunet.upv.es:443/handle/10251/100229
Some categorical aspects of the inverse limits in ditopological context
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.
2018-04-11T12:51:35ZControlled shadowing property
https://riunet.upv.es:443/handle/10251/100228
Controlled shadowing property
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.
2018-04-11T12:46:49ZCounting coarse subsets of a countable group
https://riunet.upv.es:443/handle/10251/100227
Counting coarse subsets of a countable group
Protasov, Igor; Protasova, Ksenia
[EN] For every countable group G, there are 2ω distinct classes of coarselyequivalent subsets of G.
2018-04-11T12:39:29ZRelation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions
https://riunet.upv.es:443/handle/10251/100226
Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions
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.
2018-04-11T12:35:57ZSet-open topologies on function spaces
https://riunet.upv.es:443/handle/10251/100225
Set-open topologies on function spaces
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.
2018-04-11T12:28:02Z