https://polipapers.upv.es/index.php/AGT/issue/feedApplied General Topology2018-04-11T11:37:56+02:00Applied General Topologyagt@mat.upv.esOpen Journal Systems<p style="margin-top: 0cm; margin-right: 0cm; margin-bottom: 6.0pt; margin-left: 0cm; text-align: justify; text-justify: inter-ideograph;"><span>The international journal <strong>Applied General Topology</strong> publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications.</span></p>https://polipapers.upv.es/index.php/AGT/article/view/7012Partially topological group action2018-04-10T14:34:19+02:00M. A. Al Shumranimaalshmrani1@kau.edu.saThe 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.2018-04-02T15:25:38+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7061Topological n-cells and Hilbert cubes in inverse limits2018-04-11T08:40:49+02:00Leonard R. Rubinlrubin@ou.edu<p>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 = (|K<sub>a</sub>|,p<sup>b</sup><sub>a</sub>,(A,)<a href="http://www.codecogs.com/eqnedit.php?latex=\preceq" target="_blank"><img title="\preceq" src="http://latex.codecogs.com/gif.latex?\preceq" alt="" /></a>)is an inverse system in set theory of triangulated polyhedra|K<sub>a</sub>|with simplicial bonding functions p<sup>b</sup><sub>a</sub> and X = lim X, then there exists a uniquely determined sub-inverse system X<sub>X</sub>= (|L<sub>a</sub>|, p<sup>b</sup><sub>a</sub>|L<sub>b</sub>|,(A,<a href="http://www.codecogs.com/eqnedit.php?latex=\preceq" target="_blank"><img title="\preceq" src="http://latex.codecogs.com/gif.latex?\preceq" alt="" /></a>)) of X where for each a, L<sub>a</sub> is a subcomplex of K<sub>a</sub>, each p<sup>b</sup><sub>a</sub>|L<sub>b</sub>|:|L<sub>b</sub>| → |L<sub>a</sub>| is surjective, and lim X<sub>X</sub> = 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).</p>2018-04-02T15:25:39+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7146Alternate product adjacencies in digital topology2018-04-11T08:58:31+02:00Laurence Boxerboxer@niagara.eduWe study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.2018-04-02T15:25:40+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7630Set-open topologies on function spaces2018-04-11T09:16:34+02:00Wafa Khalaf Alqurashiwafa-math@hotmail.comLiaqat Ali Khanlkhan@kau.edu.saAlexander V. Osipovoab@list.ru<p>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.</p>2018-04-02T15:25:40+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7677Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions2018-04-11T09:41:23+02:00Md Ahmadullahahmadullah2201@gmail.comMohammad Imdadmhimdad@yahoo.co.inMohammad Arifmohdarif154c@gmail.comIn 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.2018-04-02T15:25:41+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7721Counting coarse subsets of a countable group2018-04-11T09:45:04+02:00Igor Protasovi.v.protasov@gmail.comKsenia Protasovak.d.ushakova@gmail.com<p>For every countable group G, there are 2<sup>ω</sup> distinct classes of coarselyequivalent subsets of G.</p>2018-04-02T15:25:41+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7731Controlled shadowing property2018-04-11T09:48:26+02:00Alireza Zamani Bahabadizamany@um.ac.irIn 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.2018-04-02T15:25:41+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7812Some categorical aspects of the inverse limits in ditopological context2018-04-11T09:55:33+02:00Filiz Yildizyfiliz@hacettepe.edu.tr<p>This paper considers some various categorical aspects of the inverse systems (projective spectrums) and inverse limits described in the category if<strong>PDitop</strong>, 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 <strong>Inv<sub>ifPDitop</sub></strong> consisting of the inverse systems constructed by the objects and morphisms of if<strong>PDitop</strong>, 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 if<strong>PDitop</strong> and the ditopological infinite products are characterized by the finite products via inverse limits.</p>2018-04-02T15:25:42+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7849Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence2018-04-11T11:21:00+02:00Gunther Jägergunther.jaeger@hochschule-stralsund.deT. M. G. Ahsanullahtmga1@ksu.edu.saWe 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.2018-04-02T15:25:42+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7883k-semistratifiable spaces and expansions of set-valued mappings2018-04-11T11:24:58+02:00Peng-Fei Yanypengfei@sina.comXing-Yu Hu121602580@qq.comLi-Hong Xiexielihong2011@aliyun.com<p>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.</p>2018-04-02T15:25:42+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7888Few remarks on maximal pseudocompactness2018-04-11T11:27:04+02:00Angelo Bellabella@dmi.unict.it<p align="LEFT">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.</p>2018-04-02T15:25:42+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7918Fixed point theorems for nonlinear contractions with applications to iterated function systems2018-04-11T11:31:46+02:00Rajendra Pantpant.rajendra@gmail.comWe 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.2018-04-02T15:25:43+02:00Copyright (c) 2018 Applied General Topologyhttps://polipapers.upv.es/index.php/AGT/article/view/7997Some aspects of Isbell-convex quasi-metric spaces2018-04-11T11:37:56+02:00Olivier Olela Otafuduolivier.olelaotafudu@wits.ac.za<p>We introduce and investigate the concept of geodesic bicombing in T<sub>0</sub>-quasi-metric spaces. We prove that any Isbell-convex T<sub>0</sub>-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.</p>2018-04-02T15:25:43+02:00Copyright (c) 2018 Applied General Topology