Applied General Topology
https://polipapers.upv.es/index.php/AGT
<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>en-USThe works published in this journal are subject to the following terms:<br /><ol><li>The journal conserves the patrimonial rights (copyright) of the works published, and encourages and allows the reuse of the same under the license specified in point 2.</li><li>The works are published in the online edition of the journal under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0. You can copy, use, distribute, transmit and publicly display, provided acknowledgment of the authorship, the url, and the journal, and not used for commercial purposes.</li><li>The authors agree with the license used by the journal, with the conditions of self-archiving and the open access policy.</li><li>It allows authors to spread electronically (e.g., in institutional repositories or on their own website) the published version of his works, as it encourages its circulation and diffusion earliest and thus a possible increase in its citation and scope between the academic community.</li></ol>agt@mat.upv.es (Applied General Topology)ojsadmin@upvnet.upv.es (Administrador PoliPapers)Mon, 02 Apr 2018 15:25:43 +0200OJS 2.4.7.1http://blogs.law.harvard.edu/tech/rss60Partially topological group action
https://polipapers.upv.es/index.php/AGT/article/view/7012
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.M. A. Al Shumrani
Copyright (c) 2018 Applied General Topology
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https://polipapers.upv.es/index.php/AGT/article/view/7012Mon, 02 Apr 2018 15:25:38 +0200Topological n-cells and Hilbert cubes in inverse limits
https://polipapers.upv.es/index.php/AGT/article/view/7061
<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>Leonard R. Rubin
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https://polipapers.upv.es/index.php/AGT/article/view/7061Mon, 02 Apr 2018 15:25:39 +0200Alternate product adjacencies in digital topology
https://polipapers.upv.es/index.php/AGT/article/view/7146
We study properties of Cartesian products of digital images, using a variety of adjacencies that have appeared in the literature.Laurence Boxer
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https://polipapers.upv.es/index.php/AGT/article/view/7146Mon, 02 Apr 2018 15:25:40 +0200Set-open topologies on function spaces
https://polipapers.upv.es/index.php/AGT/article/view/7630
<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>Wafa Khalaf Alqurashi, Liaqat Ali Khan, Alexander V. Osipov
Copyright (c) 2018 Applied General Topology
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https://polipapers.upv.es/index.php/AGT/article/view/7630Mon, 02 Apr 2018 15:25:40 +0200Relation-theoretic metrical coincidence and common fixed point theorems under nonlinear contractions
https://polipapers.upv.es/index.php/AGT/article/view/7677
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.Md Ahmadullah, Mohammad Imdad, Mohammad Arif
Copyright (c) 2018 Applied General Topology
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https://polipapers.upv.es/index.php/AGT/article/view/7677Mon, 02 Apr 2018 15:25:41 +0200Counting coarse subsets of a countable group
https://polipapers.upv.es/index.php/AGT/article/view/7721
<p>For every countable group G, there are 2<sup>ω</sup> distinct classes of coarselyequivalent subsets of G.</p>Igor Protasov, Ksenia Protasova
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https://polipapers.upv.es/index.php/AGT/article/view/7721Mon, 02 Apr 2018 15:25:41 +0200Controlled shadowing property
https://polipapers.upv.es/index.php/AGT/article/view/7731
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.Alireza Zamani Bahabadi
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https://polipapers.upv.es/index.php/AGT/article/view/7731Mon, 02 Apr 2018 15:25:41 +0200Some categorical aspects of the inverse limits in ditopological context
https://polipapers.upv.es/index.php/AGT/article/view/7812
<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>Filiz Yildiz
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https://polipapers.upv.es/index.php/AGT/article/view/7812Mon, 02 Apr 2018 15:25:42 +0200Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence
https://polipapers.upv.es/index.php/AGT/article/view/7849
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.Gunther Jäger, T. M. G. Ahsanullah
Copyright (c) 2018 Applied General Topology
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https://polipapers.upv.es/index.php/AGT/article/view/7849Mon, 02 Apr 2018 15:25:42 +0200k-semistratifiable spaces and expansions of set-valued mappings
https://polipapers.upv.es/index.php/AGT/article/view/7883
<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>Peng-Fei Yan, Xing-Yu Hu, Li-Hong Xie
Copyright (c) 2018 Applied General Topology
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https://polipapers.upv.es/index.php/AGT/article/view/7883Mon, 02 Apr 2018 15:25:42 +0200Few remarks on maximal pseudocompactness
https://polipapers.upv.es/index.php/AGT/article/view/7888
<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>Angelo Bella
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https://polipapers.upv.es/index.php/AGT/article/view/7888Mon, 02 Apr 2018 15:25:42 +0200Fixed point theorems for nonlinear contractions with applications to iterated function systems
https://polipapers.upv.es/index.php/AGT/article/view/7918
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.Rajendra Pant
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https://polipapers.upv.es/index.php/AGT/article/view/7918Mon, 02 Apr 2018 15:25:43 +0200Some aspects of Isbell-convex quasi-metric spaces
https://polipapers.upv.es/index.php/AGT/article/view/7997
<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>Olivier Olela Otafudu
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https://polipapers.upv.es/index.php/AGT/article/view/7997Mon, 02 Apr 2018 15:25:43 +0200