Applied General Topology
https://polipapers.upv.es/index.php/AGT
<p style="text-align: justify; text-justify: inter-ideograph; margin: 0cm 0cm 6.0pt 0cm;">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.</p>Universitat Politècnica de Valènciaen-USApplied General Topology1576-9402<p><a href="http://creativecommons.org/licenses/by-nc-nd/4.0/" rel="license"><img src="https://polipapers.upv.es/public/site/images/ojsadmin/CC_by_nc_sa1.png" /></a></p> <p>This journal is licensed under a <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/deed.en" target="_blank" rel="noopener">Creative Commons Attribution-NonCommercial-ShareAlike- 4.0 International License</a>.</p>Lightly chaotic dynamical systems
https://polipapers.upv.es/index.php/AGT/article/view/15293
<p>In this paper we introduce some weak dynamical properties by using subbases for the phase space. Among them, the notion of <em>light chaos</em> is the most significant. Several examples, which clarify the relationships between this kind of chaos and some classical notions, are given. Particular attention is also devoted to the connections between the dynamical properties of a system and the dynamical properties of the associated functional envelope. We show, among other things, that a continuous map f : X → X , where X is a metric space, is chaotic (in the sense of Devaney) if and only if the associated functional dynamical system is lightly chaotic.</p>Annamaria Miranda
Copyright (c) 2024 Applied General Topology
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2024-10-012024-10-0125227728910.4995/agt.2024.15293Graded pseudo weakly prime spectrum of graded topological modules
https://polipapers.upv.es/index.php/AGT/article/view/19074
<p>In this study, we introduce graded pseudo weakly prime submodules of G-graded R-modules, which are an extension of graded weakly prime ideals over G-graded rings. On the graded spectrum of graded pseudo weakly prime submodules, we investigate the Zariski topology. Different aspects of this topological space are investigated, and they are linked to the algebraic properties of the G-graded R-modules under study.</p>Tamem Al-ShormanMalik BatainehMelis BolatBayram Ali Ersoy
Copyright (c) 2024 Tamem Al-Shorman, Malik Bataineh, Melis Bolat, Bayram Ali Ersoy
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2024-10-012024-10-0125229130310.4995/agt.2024.19074T_0 functional Alexandroff topologies are partial metrizable
https://polipapers.upv.es/index.php/AGT/article/view/19401
<p>If f : X → X is a function, the associated functional Alexandroff topology on X is the topology whose closed sets are { A ⊆ X : f ( A ) ⊆ A } . We prove that every functional Alexandroff topology is pseudopartial metrizable and every T<sub>0</sub> functional Alexandroff topology is partial metrizable. </p>Homeira Pajoohesh
Copyright (c) 2024 Homeira Pajoohesh
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2024-10-012024-10-0125230531910.4995/agt.2024.19401Mizoguchi-Takahashi local contractions to Feng-Liu contractions
https://polipapers.upv.es/index.php/AGT/article/view/19619
<p>In this article, we establish that any uniformly local Mizoguchi-Takahashi contraction is actually a set-valued contraction due to Feng and Liu on a metrically convex complete metric space. Through an example, we demonstrate that this result need not hold on any arbitrary metric space. Furthermore, when the metric space is compact, we derive that any Mizoguchi-Takahashi local contraction and Nadler local contraction are equivalent. Moreover, a result related to invariant best approximation is established.</p>Pallab MaitiAsrifa Sultana
Copyright (c) 2024 Pallab Maiti, Asrifa Sultana
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2024-10-012024-10-0125232132910.4995/agt.2024.19619On maximal nowhere dense sublocales
https://polipapers.upv.es/index.php/AGT/article/view/19797
<p>The aim of this paper is to study some variants of nowhere dense sublocales called maximal nowhere dense and homogeneous maximal nowhere dense sublocales. These concepts were initially introduced by Veksler in classical topology. We give some general properties of these sublocales and further examine their relationship with both inaccessible sublocales and remote sublocales. It turns out that a locale has all of its non-void nowhere dense sublocales maximal nowhere dense precisely when all of its its non-void nowhere dense sublocales are inaccessible. We show that the Booleanization of a locale is inaccessible with respect to every dense and open sublocale. In connection to remote sublocales, we prove that, if the supplement of an open dense sublocale S is homogeneous maximal nowhere dense, then every S<sup>#</sup>-remote sublocale is <sup>*</sup>-remote from S. Every open localic map that sends dense elements to dense elements preserves and reflects maximal nowhere dense sublocales. If such a localic map is further injective, then it sends homogeneous maximal nowhere dense sublocales back and forth.</p>Mbekezeli Nxumalo
Copyright (c) 2024 Mbekezeli Nxumalo
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2024-10-012024-10-0125233136110.4995/agt.2024.19797Some results on weaker forms of starn-CCC, weakly Lindelöf and starn-DCCC spaces
https://polipapers.upv.es/index.php/AGT/article/view/19808
<p>In this paper we provide some general results about topological spaces X which satisfy star<sup>n</sup>- <em>P</em> , weakly star<sup>n</sup>- <em>P</em> and almost star<sup>n</sup>- <em>P</em>, for <em>P</em>∈ { κ ᴄᴄ , W κ L , ᴅ κ ᴄᴄ } , where κ is an infinite cardinal number. <br />The particular cases when κ = ω , <em>P</em> ∈ { ᴄᴄᴄ , weakly Lindelöf , ᴅ ᴄᴄᴄ } are obtained. Furthermore, for the same classes of spaces defined by such <em>P</em>, by applying Erdős-Radó's theorem and using the rank <em>l</em>-diagonal notion, we establish some cardinal inequalities.</p>Ricardo Cruz-CastilloAlejandro Ramírez-PáramoJesús F. Tenorio
Copyright (c) 2024 Ricardo Cruz-Castillo, Alejandro Ramírez-Páramo, Jesús F. Tenorio
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2024-10-012024-10-0125236337410.4995/agt.2024.19808k-spaces of non-domain-valued geometric points
https://polipapers.upv.es/index.php/AGT/article/view/19887
<p>The aim of this paper is to study the topological properties of algebraic sets with zero divisors. We impose a subbasic topology on the set of proper ideals of a k-algebra and this new “k-space” becomes a generalization of the corresponding Zariski space. We prove that a k-space is T<sub>0</sub>, quasi-compact, spectral, and connected. Moreover, we study continuous maps between such k-spaces. We conclude with a question about the construction of a sheaf of k-spaces similar to affine schemes.</p>Amartya Goswami
Copyright (c) 2024 Amartya Goswami
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2024-10-012024-10-0125237538310.4995/agt.2024.19887On the hyperspaces of meager and regular continua
https://polipapers.upv.es/index.php/AGT/article/view/20116
<p>Given a metric continuum X, we consider the collection of all regular subcontinua of X and the collection of all meager subcontinua of <em>X</em>, these hyperspaces are denoted by D(X) and M(X), respectively. It is known that D(X) is compact if and only if D(X) is finite.<br />In this way, we find some conditions related about the cardinality of D(X) and we reduce the fact to count the elements of D(X) to a Graph Theory problem, as an application of this, we prove in particular that | D ( X ) | ∉ { 2,3,4,5,8 , 9 } h t ) for any continuum X. Also, we prove that D(X) is never homeomorphic to ℕ . On the other hand, given a point p ∈ X , we consider the meager composant and the filament composant of p in X, denoted by M<sup>X</sup><sub>p</sub> and Fcs<sub>X</sub>(p), respectively, and we study some relations between M<sup>X</sup><sub>p</sub> and Fcs<sub>X</sub>(p) such as the equality of them as a subset of <em>X</em>. Also, we construct examples showing that the collection Fcs ( X ) = { Fcs<sub>X</sub> ( p ) : p ∈ X } can be homeomorphic to: any finite discrete space, the harmonic sequence, the closure of the harmonic sequence and the Cantor set. Finally, we study the contractibility of M(X); we prove the arc of pseudo-arcs, which is a no contractible continuum, satisfies that its hyperspace of meager subcontinua is contractible, given a solution to an open problem. Also, we rise open problems.</p>Javier CamargoNorberto OrdoñezDiego Ramírez
Copyright (c) 2024 Javier Camargo, Norberto Ordoñez, Diego Ramírez
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2024-10-012024-10-0125238540610.4995/agt.2024.20116On star Rothberger spaces modulo an ideal
https://polipapers.upv.es/index.php/AGT/article/view/20464
<p>In this article, we introduce the ideal star-Rothberger property by coupling the notion of a star operator to that of an ideal Rothberger space, after which some of its topological characteristics are analysed. By creating relationships between a numbers of topological features with structures similar to the ideal star-Rothberger space, we reinforce the concept. In order to illustrate the differences between a number of related topological properties, we also provide several counter examples. Certain preservation-related properties under subspaces and functions are investigated. Lastly we find a way to express ideal star-Rothberger space by means of families of closed sets by bringing some modifications to the SSI^I property. </p>Susmita SarkarPrasenjit BalMithun Datta
Copyright (c) 2024 Susmita Sarkar, Prasenjit Bal, Mithun Datta
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2024-10-012024-10-0125240741410.4995/agt.2024.20464Withdrawn
https://polipapers.upv.es/index.php/AGT/article/view/20646
<p><em>The editorial board has withdrawn this article since we have been warned that one of the authors' names has been added without his permission. </em></p> <p><em>Maintaining ethical standards is a priority for our journal, and adding an author who did not contribute to the research or writing of the manuscript contravenes the conditions of the agreement of cession signed by the authors. </em></p> <p><em>The Publisher apologizes for any inconvenience this may cause.</em></p>Applied General Topology
Copyright (c) 2024
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2024-10-012024-10-0125241542110.4995/agt.2024.20646Existence of fixed points of large MR-Kannan contractions in Banach Spaces
https://polipapers.upv.es/index.php/AGT/article/view/20852
<p>The purpose of this paper is to introduce the class of large MR-Kannan contractions on Banach space that contains the classes of Kannan, enriched Kannan, large Kannan, MR-Kannan contractions and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. We prove the existence of a unique fixed point for such a class of operators in Banach spaces.</p>Rizwan AnjumMujahid AbbasMuhammad Waqar AkramStojan Radenović
Copyright (c) 2024 Rizwan Anjum, Mujahid Abbas, Muhammad Waqar Akram, Stojan Radenović
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2024-10-012024-10-0125242343910.4995/agt.2024.20852H-partial uniform spaces and their application in the compression of digital images
https://polipapers.upv.es/index.php/AGT/article/view/20973
<p>Fixed point theorem is very important tool in different branches of mathematics. In this paper, we introduce partial uniform spaces as a generalization of uniform spaces and metric spaces; and study some basic properties. Various examples support the theory. We prove fixed point theorems for H-partial uniform spaces, by using a mapping called E-distance function. Finally, we give the applications of these fixed point theorems to compress digital images.</p>Satya Narayan ShuklaSurabhi Tiwari
Copyright (c) 2024 Satya Narayan Shukla, Surabhi Tiwari
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2024-10-012024-10-0125244145610.4995/agt.2024.20973Remarks on fixed point assertions in digital topology, 8
https://polipapers.upv.es/index.php/AGT/article/view/21074
<p>This paper continues a series in which we study deficiencies in previously published works concerning fixed point assertions for digital images.</p>Laurence Boxer
Copyright (c) 2024 Laurence Boxer
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2024-10-012024-10-0125245747310.4995/agt.2024.21074An interpolative class of two-Lipschitz mappings of composition type
https://polipapers.upv.es/index.php/AGT/article/view/21116
<p>The paper deals with some further results concerning the class of two-Lipschitz operators. We prove first an isometric isomorphism<br />identification of two-Lipschitz operators and Lipschitz operators. After defining and characterizing the adjoint of a two-Lipschitz operator, we prove a Schauder type theorem on the compactness of the adjoint. We study the extension of two-Lipschitz operators from the cartesian product of two complemented subspaces of a Banach space to the cartesian product of whole spaces. Also, we show that every two-Lipschitz functional defined on the cartesian product of two pointed metric spaces admits an extension with the same two-Lipschitz norm under some requirements on domaine spaces.</p>Khaled HamidiAbdelhamid Tallab
Copyright (c) 2024 Khaled Hamidi, Abdelhamid Tallab
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2024-10-012024-10-0125247548910.4995/agt.2024.21116A generalization of strongly irreducible ideals with a view towards rings of continuous functions
https://polipapers.upv.es/index.php/AGT/article/view/21264
<p>In this note, we introduce and study the concept of a semi-strongly irreducible ideal, a natural generalization of a strongly irreducible ideal. We say an ideal I of a commutative ring R is <em>semi-strongly irreducible</em> if for ideals J and K of R, the inclusion J ∩ K ⊆ I implies that either J<sup>2</sup> ⊆ I or K<sup>2</sup> ⊆ I . After some general results, the article focuses on semi-strongly irreducible ideals in rings of continuous functions.</p>Jamal HashemiHossein Yari
Copyright (c) 2024 Jamal Hashemi, Hossein Yari
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2024-10-012024-10-0125249150110.4995/agt.2024.21264Butterfly points and hyperspace selections
https://polipapers.upv.es/index.php/AGT/article/view/21302
<p>If f is a continuous selection for the Vietoris hyperspace ℱ(X) of the nonempty closed subsets of a space X, then the point f(X)∊ X is not as arbitrary as it might seem at first glance. In this paper, we will characterise these points by local properties at them. Briefly, we will show that p=f(X) is a strong butterfly point precisely when it has a countable clopen base in cl(U) for some open set U⊂ X\{p} with cl(U)=U ∪ {p}. Moreover, the same is valid when X is totally disconnected at p=f(X) and p is only assumed to be a butterfly point. This gives the complete affirmative solution to a question raised previously by the author. Finally, when p=f(X) lacks the above local base-like property, we will show that ℱ(X) has a continuous selection h with the stronger property that h(S)=p for every closed S⊂X with p∈S.</p>Valentin Gutev
Copyright (c) 2024 Valentin Gutev
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2024-10-012024-10-0125250351710.4995/agt.2024.21302On traditional Menger and Rothberger variations
https://polipapers.upv.es/index.php/AGT/article/view/21437
<p>We present a comprehensive report on the relationships between variations of the Menger and Rothberger selection properties with respect to w-covers and k-covers in the most general topological setting and address the finite productivity of some of these properties. We collect various examples that separate certain properties and we carefully identify which separation axioms simplify aspects of these properties. We finish with a consolidated list of open questions focused on topological examples.</p>Christopher CaruvanaSteven ClontzJared Holshouser
Copyright (c) 2024 Christopher Caruvana, Steven Clontz, Jared Holshouser
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2024-10-012024-10-0125251955210.4995/agt.2024.21437