https://ojs.cc.upv.es/index.php/AGT/issue/feedApplied General Topology2024-04-02T11:09:35+02:00Applied General Topologyagt@mat.upv.esOpen Journal Systems<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>https://ojs.cc.upv.es/index.php/AGT/article/view/19855Expansive homeomorphisms on quasi-metric spaces2023-09-15T09:21:48+02:00Olivier Olela Otafuduolmaolela@gmail.comDibona Peggy Matladidibona.matladi@ul.ac.zaMcedisi Sphiwe Zwenisphiwedicy@gmail.com<p>The investigation of expansive homeomorphisms in metric spaces began with Utz in 1950. Thereafter, several authors have extensively studied this concept for different motivations. In this current article, we study expansive homeomorphism in the context of quasi-pseudometric spaces. This is motivated by the fact that any expansive homeomorphism on quasi-pseudometric space is again expansive homeomorphism on its induced pseudometric space but the converse is not true in general. Moreover, the study of orbit structures has been taken to consideration in this article. For instance, we investigate the denseness of orbits in the context of quasi-metric spaces.</p>2024-04-02T00:00:00+02:00Copyright (c) 2023 Applied General Topologyhttps://ojs.cc.upv.es/index.php/AGT/article/view/20590Common fixed point theorems on complete and weak G-complete fuzzy metric spaces2023-12-21T09:12:24+01:00Sugata Adhyasugataadhya@yahoo.comA. Deb Rayderayatasi@gmail.com<p>Motivated by Gopal and Vetro, we introduce a symmetric pair of β-admissible mappings and obtain common fixed point theorems for such a pair in complete and weak G-complete fuzzy metric spaces. In particular, we rectified, generalize and improve the common fixed point theorem obtained by Turkoglu and Sangurlu for two fuzzy ψ-contractive mappings. We include non-trivial examples to exhibit the generality and demonstrate our results.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Sugata Adhya, A. Deb Rayhttps://ojs.cc.upv.es/index.php/AGT/article/view/20461On σ-compact Hattori spaces2023-11-27T17:21:20+01:00Vitalij A. Chatyrkovitalij.tjatyrko@liu.se<pre> We present several characterizations of σ-compact Hattori spaces, and reject some possible characterization candidates of the spaces.</pre>2024-04-02T00:00:00+02:00Copyright (c) 2024 Vitalij Chatyrkohttps://ojs.cc.upv.es/index.php/AGT/article/view/20387On some questions on selectively highly divergent spaces2023-09-25T10:51:57+02:00Angelo Bellabella@dmi.unict.itSanti Spadarosantidomenico.spadaro@unipa.it<p>A topological space X is selectively highly divergent (SHD) if for every sequence of non-empty open sets { U<sub>n</sub> : n ∈ ω } of X, we can find x<sub>n</sub> ∈ U<sub>n</sub> such that the sequence {x<sub>n</sub> : n ∈ ω } has no convergent subsequences. In this note we answer two questions related to this notion asked by Jiménez-Flores, Ríos-Herrejón, Rojas-Sánchez and Tovar-Acosta.</p>2024-04-02T00:00:00+02:00Copyright (c) 2023 Angelo Bella, Santi Spadarohttps://ojs.cc.upv.es/index.php/AGT/article/view/20296The extension of two-Lipschitz operators2023-09-11T12:38:09+02:00Elhadj Dahiahajdahia@gmail.com<p>The paper deals with some further results concerning the class of two-Lipschitz operators. We prove first an isometric isomorphism identification of two-Lipschitz operators and Lipschitz operators. After defining and characterize the adjoint of two-Lipschitz operator, we prove a Schauder type theorem on the compactness of the adjoint. We study the extension of two-Lipschitz operators from 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 cartesian product of two pointed metric spaces admits an extension with the same two-Lipschitz norm, under some requirements on domaine spaces.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Elhadj Dahiahttps://ojs.cc.upv.es/index.php/AGT/article/view/20267Homomorphisms of the lattice of slowly oscillating functions on the half-line2023-09-11T01:54:15+02:00Yutaka Iwamotoy.iwamoto@niihama-nct.ac.jp<div> <div>We study the space H(SO) of all homomorphisms of the vector lattice of all slowly oscillating functions on the half-line ℍ = [ 0 , ∞ ) . In contrast to the case of homomorphisms of uniformly continuous functions, it is shown that a homomorphism in H(SO) which maps the unit to zero must be zero-homomorphism. Consequently, we show that the space H(SO) without zero-homomorphism is homeomorphic to ℍ x (0, ∞). By describing a neighborhood base of zero-homomorphism, we show that H(SO) is homeomorphic to the space ℍ x (0, ∞) with one point added.</div> </div>2024-04-02T00:00:00+02:00Copyright (c) 2024 Yutaka Iwamotohttps://ojs.cc.upv.es/index.php/AGT/article/view/20224Fixed point approximations via generalized MR-Kannan mappings in Banach spaces2023-08-24T19:27:41+02:00Ravindra K. Bishtravindra.bisht@yahoo.comJay Singhmathjaysingh84@gmail.com<p>In this paper, we introduce a generalization of the concept of MR-Kannan type contractions and utilize this condition to derive new fixed point theorems under both contractive and non-contractive conditions. Our approach enhances various existing results related to enriched mappings.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Ravindra Bisht, Jay Singhhttps://ojs.cc.upv.es/index.php/AGT/article/view/20211Iterated function system of generalized cyclic F-contractive mappings2023-08-20T20:07:18+02:00Talat Nazirdr.talatnazir@gmail.comMujahid Abbasabbas.mujahid@gmail.comHira Haleem Lodhihirahaleem525@gmail.com<p>The aim of this paper is to study the sufficient conditions for the existence of attractor of a generalized cyclic iterated function system composed of a complete metric space and a finite collection of generalized cyclic F-contraction mappings. Some examples are presented to support our main results and concepts defined herein. The results proved in the paper extend and generalize various well known results in the existing literature.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Talat Nazir, Mujahid Abbas, Hira Haleem Lodhihttps://ojs.cc.upv.es/index.php/AGT/article/view/20026Remarks on fixed point assertions in digital topology, 72023-07-14T13:14:29+02:00Laurence Boxerlaurence.boxer@gmail.com<p>This paper continues a series discussing flaws in published assertions concerning fixed points in digital images.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Laurence Boxerhttps://ojs.cc.upv.es/index.php/AGT/article/view/19885On interpolative Hardy-Rogers type cyclic contractions2023-08-28T00:01:41+02:00Mohamed Edraouiedraoui.mohamed@gmail.comAmine El koufiamine.elkoufi@uit.ac.maMohamed Aamriaamrimohamed9@yahoo.fr<p>Recently, Karapınar introduced a new Hardy-Rogers type contractive mapping using the concept of interpolation and proved a fixed point theorem in complete metric space. This new type of mapping, called "interpolative Hardy-Rogers type contractive mapping" is a generalization of Hardy-Rogers's fixed point theorem. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for cyclic mappings on complete metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Mohamed Edraoui, Amine El koufi, Mohamed Aamrihttps://ojs.cc.upv.es/index.php/AGT/article/view/17810Partial actions on quotient spaces and globalization2023-03-10T13:06:04+01:00Luis Martínezluchomartinez9816@hotmail.comHéctor Pinedohpinedot@uis.edu.coAndrés Villamizarandresvillamizar1793@hotmail.com<p>Given a partial action of a topological group G on a space X we determine properties P which can be extended from X to its globalization. We treat the cases when P is any of the following: Hausdorff, regular, metrizable, second countable, and having invariant metric. Further, for a normal subgroup H, we introduce and study a partial action of G/H on the orbit space of X; applications to invariant metrics and inverse limits are presented.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Luis Martínez, Héctor Pinedo, Andrés Villamizarhttps://ojs.cc.upv.es/index.php/AGT/article/view/18049Partial actions of groups on profinite spaces2023-09-14T09:09:46+02:00Luis Martínezluchomartinez9816@hotmail.comHéctor Pinedohpinedot@uis.edu.coAndrés Villamizarandresvillamizar1793@hotmail.com<p>We show that for a partial action η with closed domain of a compact group G on a profinite space X the space of orbits X/~<sub>G</sub> is profinite, this leads to the fact that when G is profinite the enveloping space X<sub>G</sub> is also profinite. Moreover, we provide conditions for the induced quotient map π<sub>G</sub> : X → X / ∼<sub>G</sub> of η to have a continuous section. Relations between continuous sections of π<sub>G</sub> and continuous sections of the quotient map induced by the enveloping action of η are also considered. At the end of this work, we prove that the category of actions on profinite spaces with countable number of clopen sets is reflective in the category of actions of compact Hausdorff spaces having countable number of clopen sets.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Luis Martínez, Héctor Pinedo, Andrés Villamizarhttps://ojs.cc.upv.es/index.php/AGT/article/view/19798Some existence and uniqueness results for a solution of a system of equations2023-09-17T15:52:32+02:00Deepak Khantwaldeepakkhantwal15@gmail.comRajendra Pantpant.rajendra@gmail.com<p>This paper presents some existence and uniqueness results for a solution of a system of equations. Our results extend and generalize the well-known and celebrated results of Boyd and Wong [Proc. Amer. Math. Soc. 20 (1969)], Matkowski [Dissertations Math.(Rozprawy Mat.) 127 (1975)], Proinov [Nonlinear Anal. 64 (2006)], Ri [Indag. Math. (N. S.) 27 (2016)] and many others. We also present some illustrative examples to validate our results.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Deepak Khantwal, Rajendra Panthttps://ojs.cc.upv.es/index.php/AGT/article/view/19780Hemi metric spaces and Banach fixed point theorems2023-05-25T23:19:04+02:00Vildan Ozturkvildan_ozturk@hotmail.comStojan Radenovicradens@beotel.net<p>In this work, we will define a new type metric with degree m and m+1 points which is called m-hemi metric as a generalization of two metric spaces. We will give and prove some topological properties. Also, Banach contraction mapping principle were proved and a application to Fredholm integral equation were gived in hemi metric spaces.</p>2024-04-02T00:00:00+02:00Copyright (c) 2023 Applied General Topologyhttps://ojs.cc.upv.es/index.php/AGT/article/view/19760A study of new dimensions for ideal topological spaces2023-05-23T10:11:31+02:00Fotini Seretiseretifot@gmail.com<p>In this paper new notions of dimensions for ideal topological spaces are inserted, called *-quasi covering dimension and ideal quasi<br />covering dimension. We study several of their properties and investigate their relations with types of covering dimensions like the *-covering dimension and the ideal covering dimension.</p>2024-04-02T00:00:00+02:00Copyright (c) 2023 Applied General Topologyhttps://ojs.cc.upv.es/index.php/AGT/article/view/19400Compactness in the endograph uniformity2023-05-09T11:10:08+02:00Iván Sánchezisr.uami@gmail.com<pre>Given a uniform space (X,U), we denote by F<sup>*</sup>(X) to the family of fuzzy sets u in (X,U) such that u is normal and upper semicontinuous. Let U<sub>E</sub> be the endograph uniformity on F<sup>*</sup>(X). In this paper, we mainly characterize totally bounded and compact substes in the uniform space (F<sup>*</sup>(X),U<sub>E</sub>).<br /><br /></pre> <p> </p>2024-04-02T00:00:00+02:00Copyright (c) 2023 Applied General Topologyhttps://ojs.cc.upv.es/index.php/AGT/article/view/19371The degree of nondensifiability of linear bounded operators and its applications2023-09-05T22:28:09+02:00Gonzalo Garcíagonzalogarciamacias@gmail.comGaspar Moragaspar.mora@facen.una.py<p>In the present paper we define the degree of nondensifiability (DND for short) of a bounded linear operator T on a Banach space and analyze its properties and relations with the Hausdorff measure of non-compactness (MNC for short) of T. As an application of our results, we have obtained a formula to find the essential spectral radius of a bounded operator T on a Banach space as well as we have provided the best possible lower bound for the Hyers-Ulam stability constant of T in terms of the aforementioned DND.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Gonzalo García, Gaspar Morahttps://ojs.cc.upv.es/index.php/AGT/article/view/18989On topological groups of monotonic automorphisms2023-12-05T11:45:45+01:00Raushan BuzyakovaRaushan_Buzyakova@yahoo.com<p>We study topological groups of monotonic automorphisms on a generalized ordered space L. We find a condition that is necessary and sufficient for the set of all monotonic automorphism on L along with the function composition and the topology of point-wise convergence to be a topological group.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Raushan Buzyakovahttps://ojs.cc.upv.es/index.php/AGT/article/view/18928Strongly Lipschitz (ℓp ,ℓq)-factorable mappings2023-10-07T19:30:15+02:00Dahmane Achourdahmane.achour@univ-msila.dzToufik Tiaibatoufik.tiaiba@univ-msila.dz<p>In this paper we study the space of strongly Lipschitz (ℓ<sub>p</sub> ,ℓ<sub>q</sub>) -factorable operators between metric spaces and a Banach spaces. In particular, a factorization of this class through ℓ<sub>p</sub> and ℓ<sub>q</sub> spaces is given. We show that this type of operators fits in the theory of composition α-Banach Lipschitz operator ideal. As a special case, we get a Lipschitz version of weakly p-nuclear operators.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Dahmane Achour, Toufik Tiaibahttps://ojs.cc.upv.es/index.php/AGT/article/view/18884Pointwise convergence on the rings of functions which are discontinuous on a set of measure zero2023-02-16T17:28:23+01:00Dhananjoy Mandaldmandal.cu@gmail.comAchintya Singhaachintya.puremath@gmail.comSagarmoy Bagsagarmoy.bag01@gmail.com<p>Consider the ring ℳ<sub>∘</sub> ( X , μ ) of functions which are discontinuous on a set of measure zero which is introduced and studied extensively in [2]. In this paper, we have introduced a ring B<sub>1</sub> ( X , μ ) of functions which are pointwise limits of sequences of functions in ℳ<sub>∘</sub> ( X , μ ) . We have studied various properties of zero sets, B<sub>1</sub> ( X , μ ) -separated and B<sub>1</sub> ( X , μ ) -embedded subsets of B<sub>1</sub> ( X , μ ) and also established an analogous version of Urysohn's extension theorem. We have investigated a connection between ideals of B<sub>1</sub> ( X , μ ) and Z<sub>B</sub> -filters on X. We have studied an analogue of Gelfand-Kolmogoroff theorem in our setting. We have defined real maximal ideals of B<sub>1</sub> ( X , μ ) and established the result | ℛ M a x ( ℳ<sub>∘</sub> ( X , μ ) ) | = | ℛ M a x ( B<sub>1</sub> ( X , μ ) ) | , where ℛ M a x ( ℳ<sub>∘</sub> ( X , μ ) ) and ℛ M a x ( B<sub>1</sub> ( X , μ ) ) are the sets of all real maximal ideals of ℳ<sub>∘</sub> ( X , μ ) and B<sub>1</sub> ( X , μ ) respectively.</p>2024-04-02T00:00:00+02:00Copyright (c) 2024 Dhananjoy Mandal, Achintya Singha, Sagarmoy Bag