Applied General Topology <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 València en-US Applied General Topology 1576-9402 <p><a href="" rel="license"><img src="" /></a></p> <p>This journal is licensed under a <a href="" target="_blank" rel="noopener">Creative Commons Attribution-NonCommercial-ShareAlike- 4.0 International License</a>.</p> Expansive homeomorphisms on quasi-metric spaces <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> Olivier Olela Otafudu Dibona Peggy Matladi Mcedisi Sphiwe Zweni Copyright (c) 2023 Applied General Topology 2024-04-02 2024-04-02 25 1 1 15 10.4995/agt.2024.19855 Common fixed point theorems on complete and weak G-complete fuzzy metric spaces <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> Sugata Adhya A. Deb Ray Copyright (c) 2024 Sugata Adhya, A. Deb Ray 2024-04-02 2024-04-02 25 1 17 34 10.4995/agt.2024.20590 On σ-compact Hattori spaces <pre> We present several characterizations of σ-compact Hattori spaces, and reject some possible characterization candidates of the spaces.</pre> Vitalij A. Chatyrko Copyright (c) 2024 Vitalij Chatyrko 2024-04-02 2024-04-02 25 1 35 40 10.4995/agt.2024.20461 On some questions on selectively highly divergent spaces <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> Angelo Bella Santi Spadaro Copyright (c) 2023 Angelo Bella, Santi Spadaro 2024-04-02 2024-04-02 25 1 41 46 10.4995/agt.2024.20387 The extension of two-Lipschitz operators <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> Elhadj Dahia Copyright (c) 2024 Elhadj Dahia 2024-04-02 2024-04-02 25 1 47 56 10.4995/agt.2024.20296 Homomorphisms of the lattice of slowly oscillating functions on the half-line <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> Yutaka Iwamoto Copyright (c) 2024 Yutaka Iwamoto 2024-04-02 2024-04-02 25 1 57 70 10.4995/agt.2024.20267 Fixed point approximations via generalized MR-Kannan mappings in Banach spaces <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> Ravindra K. Bisht Jay Singh Copyright (c) 2024 Ravindra Bisht, Jay Singh 2024-04-02 2024-04-02 25 1 71 77 10.4995/agt.2024.20224 Iterated function system of generalized cyclic F-contractive mappings <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> Talat Nazir Mujahid Abbas Hira Haleem Lodhi Copyright (c) 2024 Talat Nazir, Mujahid Abbas, Hira Haleem Lodhi 2024-04-02 2024-04-02 25 1 79 96 10.4995/agt.2024.20211 Remarks on fixed point assertions in digital topology, 7 <p>This paper continues a series discussing flaws in published assertions concerning fixed points in digital images.</p> Laurence Boxer Copyright (c) 2024 Laurence Boxer 2024-04-02 2024-04-02 25 1 97 115 10.4995/agt.2024.20026 On interpolative Hardy-Rogers type cyclic contractions <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> Mohamed Edraoui Amine El koufi Mohamed Aamri Copyright (c) 2024 Mohamed Edraoui, Amine El koufi, Mohamed Aamri 2024-04-02 2024-04-02 25 1 117 124 10.4995/agt.2024.19885 Partial actions on quotient spaces and globalization <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> Luis Martínez Héctor Pinedo Andrés Villamizar Copyright (c) 2024 Luis Martínez, Héctor Pinedo, Andrés Villamizar 2024-04-02 2024-04-02 25 1 125 141 10.4995/agt.2024.17810 Partial actions of groups on profinite spaces <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> Luis Martínez Héctor Pinedo Andrés Villamizar Copyright (c) 2024 Luis Martínez, Héctor Pinedo, Andrés Villamizar 2024-04-02 2024-04-02 25 1 143 157 10.4995/agt.2024.18049 Some existence and uniqueness results for a solution of a system of equations <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> Deepak Khantwal Rajendra Pant Copyright (c) 2024 Deepak Khantwal, Rajendra Pant 2024-04-02 2024-04-02 25 1 159 174 10.4995/agt.2024.19798 Hemi metric spaces and Banach fixed point theorems <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> Vildan Ozturk Stojan Radenovic Copyright (c) 2023 Applied General Topology 2024-04-02 2024-04-02 25 1 175 182 10.4995/agt.2024.19780 A study of new dimensions for ideal topological spaces <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> Fotini Sereti Copyright (c) 2023 Applied General Topology 2024-04-02 2024-04-02 25 1 183 198 10.4995/agt.2024.19760 Compactness in the endograph uniformity <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> Iván Sánchez Copyright (c) 2023 Applied General Topology 2024-04-02 2024-04-02 25 1 199 211 10.4995/agt.2024.19400 The degree of nondensifiability of linear bounded operators and its applications <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> Gonzalo García Gaspar Mora Copyright (c) 2024 Gonzalo García, Gaspar Mora 2024-04-02 2024-04-02 25 1 213 228 10.4995/agt.2024.19371 On topological groups of monotonic automorphisms <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> Raushan Buzyakova Copyright (c) 2024 Raushan Buzyakova 2024-04-02 2024-04-02 25 1 229 235 10.4995/agt.2024.18989 Strongly Lipschitz (ℓp ,ℓq)-factorable mappings <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> Dahmane Achour Toufik Tiaiba Copyright (c) 2024 Dahmane Achour, Toufik Tiaiba 2024-04-02 2024-04-02 25 1 237 251 10.4995/agt.2024.18928 Pointwise convergence on the rings of functions which are discontinuous on a set of measure zero <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> Dhananjoy Mandal Achintya Singha Sagarmoy Bag Copyright (c) 2024 Dhananjoy Mandal, Achintya Singha, Sagarmoy Bag 2024-04-02 2024-04-02 25 1 253 275 10.4995/agt.2024.18884