Applied General Topology 2024-04-02T11:09:35+02:00 Applied General Topology Open 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> Expansive homeomorphisms on quasi-metric spaces 2023-09-15T09:21:48+02:00 Olivier Olela Otafudu Dibona Peggy Matladi Mcedisi Sphiwe Zweni <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+02:00 Copyright (c) 2023 Applied General Topology Common fixed point theorems on complete and weak G-complete fuzzy metric spaces 2023-12-21T09:12:24+01:00 Sugata Adhya A. Deb Ray <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+02:00 Copyright (c) 2024 Sugata Adhya, A. Deb Ray On σ-compact Hattori spaces 2023-11-27T17:21:20+01:00 Vitalij A. Chatyrko <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+02:00 Copyright (c) 2024 Vitalij Chatyrko On some questions on selectively highly divergent spaces 2023-09-25T10:51:57+02:00 Angelo Bella Santi Spadaro <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+02:00 Copyright (c) 2023 Angelo Bella, Santi Spadaro The extension of two-Lipschitz operators 2023-09-11T12:38:09+02:00 Elhadj Dahia <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+02:00 Copyright (c) 2024 Elhadj Dahia Homomorphisms of the lattice of slowly oscillating functions on the half-line 2023-09-11T01:54:15+02:00 Yutaka Iwamoto <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+02:00 Copyright (c) 2024 Yutaka Iwamoto Fixed point approximations via generalized MR-Kannan mappings in Banach spaces 2023-08-24T19:27:41+02:00 Ravindra K. Bisht Jay Singh <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+02:00 Copyright (c) 2024 Ravindra Bisht, Jay Singh Iterated function system of generalized cyclic F-contractive mappings 2023-08-20T20:07:18+02:00 Talat Nazir Mujahid Abbas Hira Haleem Lodhi <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+02:00 Copyright (c) 2024 Talat Nazir, Mujahid Abbas, Hira Haleem Lodhi Remarks on fixed point assertions in digital topology, 7 2023-07-14T13:14:29+02:00 Laurence Boxer <p>This paper continues a series discussing flaws in published assertions concerning fixed points in digital images.</p> 2024-04-02T00:00:00+02:00 Copyright (c) 2024 Laurence Boxer On interpolative Hardy-Rogers type cyclic contractions 2023-08-28T00:01:41+02:00 Mohamed Edraoui Amine El koufi Mohamed Aamri <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+02:00 Copyright (c) 2024 Mohamed Edraoui, Amine El koufi, Mohamed Aamri Partial actions on quotient spaces and globalization 2023-03-10T13:06:04+01:00 Luis Martínez Héctor Pinedo Andrés Villamizar <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+02:00 Copyright (c) 2024 Luis Martínez, Héctor Pinedo, Andrés Villamizar Partial actions of groups on profinite spaces 2023-09-14T09:09:46+02:00 Luis Martínez Héctor Pinedo Andrés Villamizar <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+02:00 Copyright (c) 2024 Luis Martínez, Héctor Pinedo, Andrés Villamizar Some existence and uniqueness results for a solution of a system of equations 2023-09-17T15:52:32+02:00 Deepak Khantwal Rajendra Pant <p>This paper presents some existence and uniqueness results for a system of mappings on the finite product of metric spaces. 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)], Song-il 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+02:00 Copyright (c) 2024 Deepak Khantwal, Rajendra Pant Hemi metric spaces and Banach fixed point theorems 2023-05-25T23:19:04+02:00 Vildan Ozturk Stojan Radenovic <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+02:00 Copyright (c) 2023 Applied General Topology A study of new dimensions for ideal topological spaces 2023-05-23T10:11:31+02:00 Fotini Sereti <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+02:00 Copyright (c) 2023 Applied General Topology Compactness in the endograph uniformity 2023-05-09T11:10:08+02:00 Iván Sánchez <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+02:00 Copyright (c) 2023 Applied General Topology The degree of nondensifiability of linear bounded operators and its applications 2023-09-05T22:28:09+02:00 Gonzalo García Gaspar Mora <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+02:00 Copyright (c) 2024 Gonzalo García, Gaspar Mora On topological groups of monotonic automorphisms 2023-12-05T11:45:45+01:00 Raushan Buzyakova <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+02:00 Copyright (c) 2024 Raushan Buzyakova Strongly Lipschitz (ℓp ,ℓq)-factorable mappings 2023-10-07T19:30:15+02:00 Dahmane Achour Toufik Tiaiba <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+02:00 Copyright (c) 2024 Dahmane Achour, Toufik Tiaiba Pointwise convergence on the rings of functions which are discontinuous on a set of measure zero 2023-02-16T17:28:23+01:00 Dhananjoy Mandal Achintya Singha Sagarmoy Bag <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+02:00 Copyright (c) 2024 Dhananjoy Mandal, Achintya Singha, Sagarmoy Bag