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> Universitat Politècnica de València en-US Applied General Topology 1576-9402 <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> Countable networks on Malykhin's maximal topological group https://polipapers.upv.es/index.php/AGT/article/view/18517 <p>We present a solution to the following problem: Does every countable and non-discrete topological (Abelian) group have a countable network with infinite elements? In fact, we show that no maximal topological space allows for a countable network with infinite elements. As a result, we answer the question in the negative. The article also focuses on Malykhin's maximal topological group constructed in 1975 and establishes some unusual properties of countable networks on this special group G. We show, in particular, that for every countable network N for G, the family of finite elements of N is also a network for G.</p> Edgar Márquez Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 239 246 10.4995/agt.2023.18517 Fixed points results for various types of interpolative cyclic contraction https://polipapers.upv.es/index.php/AGT/article/view/19515 <p><span class="fontstyle0">In this paper, we introduce four new types of contractions called in this order Kannan-type cyclic contraction via interpolation, interpolative Ćirić-Reich-Rus type cyclic contraction, and we prove the existence and uniqueness for a fixed point for each situation.</span></p> Mohamed Edraoui Amine El koufi Soukaina Semami Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 247 252 10.4995/agt.2023.19515 ★-quasi-pseudometrics on algebraic structures https://polipapers.upv.es/index.php/AGT/article/view/19303 <p>In this paper, we introduce some concepts of ★-(quasi)-pseudometric spaces, and give an example which shows that there is a ★-quasi-pseudometric space which is not a quasi-pseudometric space. We also study the conditions under which ★-quasi-pseudometric semitopological groups are paratopological groups or topological groups.</p> Shi-Yao He Ying-Ying Jin Li-Hong Xie Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 253 265 10.4995/agt.2023.19303 Ćirić-generalized contraction via wt−distance https://polipapers.upv.es/index.php/AGT/article/view/19268 <p>In this present paper, besides other things, we introduce the concept of Ćirić-generalized contractions via wt−distance and then we will prove some new fixed point results for these mappings, which generalize and improve fixed point theorems by L. B. Ćirić in [9, 8, 10] and also, B. E. Rhoades in [23]. Some examples illustrate usefulness of the new results. At the end, we will give some applications to nonlinear fractional differential equations.</p> Hosein Lakzian Darko Kocev Vladimir Rakočević Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 267 280 10.4995/agt.2023.19268 Remarks on fixed point assertions in digital topology, 6 https://polipapers.upv.es/index.php/AGT/article/view/18996 <p>This paper continues a series discussing flaws in published assertions concerning fixed points in digital metric spaces.</p> Laurence Boxer Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 281 305 10.4995/agt.2023.18996 Fixed points of set-valued mappings in Menger probabilistic metric spaces endowed with an amorphous binary relation https://polipapers.upv.es/index.php/AGT/article/view/18993 <p>In this paper, we prove the existence of fixed point results for set-valued mappings in Menger probabilistic metric spaces equipped with an amorphous binary relation and a Hadžić -type t-norm. For the usability of such findings we present a Kelisky-Rivlin type result for a class of Bernstein type special operators introduced by Deo et. al. [Appl. Math. Comput. 201, (2008), 604-612 ] on the space C([ 0, n/n+1]). In this way, these investigations extend, modify and generalize some prominent recent fixed point results of the existing literature.</p> Gopi Prasad Sheetal Deshwal Rupesh K. Srivastav Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 307 322 10.4995/agt.2023.18993 Partial actions on limit spaces https://polipapers.upv.es/index.php/AGT/article/view/18665 <p>G-compactifications of continuous partial actions in the category of limit spaces are considered. In particular, sufficient conditions are given to ensure that (G, X, α) has a largest regular G-compactification.</p> Bernd Losert Gary Richardson Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 323 331 10.4995/agt.2023.18665 Rough representations of rough topological groups https://polipapers.upv.es/index.php/AGT/article/view/18577 <p>In this paper, the concept of rough representation of a rough topological group on a Banach space is explored. Mainly, the continuity and the irreducibility of rough representations are studied.</p> Essoyomewè Kieou Mawoussi Todjro Yaogan Mensah Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 333 341 10.4995/agt.2023.18577 A note on the fixed point theorem of F-contraction mappings in rectangular M-metric space https://polipapers.upv.es/index.php/AGT/article/view/18557 <p>In this note, we show that the main result (Theorem 3.2) due to Asim et al. (Appl. Gen. Topol., 23(2), 363-376 (2022) https://doi.org/10.4995/agt.2022.17418) is still valid if we remove the assumption of continuity of the mapping.</p> Mujahid Abbas Rizwan Anjum Rabia Anwar Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 343 358 10.4995/agt.2023.18557 On graph induced symbolic systems https://polipapers.upv.es/index.php/AGT/article/view/16662 <p>In this paper, we investigate shift spaces arising from a multidimensional graph G. In particular, we investigate nonemptiness and existence of periodic points for a multidimensional shift space. We derive sufficient conditions under which these questions can be answered affirmatively. We investigate the structure of the shift space using the generating matrices. We prove that any d-dimensional shift of finite type is finite if and only if it is conjugate to a shift generated through permutation matrices. We prove that if any triangular pattern of the form a b c can be extended to a 1 x 1 square then the two dimensional shift space possesses periodic points. We introduce the notion of an E-pair for a two dimensional shift space. Using the notion of an E-pair, we derive sufficient conditions for non-emptiness of the two dimensional shift space under discussion.</p> Prashant Kumar Puneet Sharma Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 359 378 10.4995/agt.2023.16662 Strong Fréchet properties of spaces constructed from squares and AD families https://polipapers.upv.es/index.php/AGT/article/view/18504 <p>We answer questions of Arhangel'skiĭ using spaces defined from combinatorial objects. We first establish further convergence properties of a space constructed from □ ( κ ) showing it is Fréchet-Urysohn for finite sets and a <em>w</em>-space that is not a <em>W</em>-space. We also show that under additional assumptions it may be not bi-sequential, and so providing a consistent example of an absolutely Fréchet α<sub>1</sub> space that is not bisequential. In addition, if we do not require the space being α<sub>1</sub>, we can construct a ZFC example of a countable absolutely Fréchet space that is not bisequential from an almost disjoint family of subsets of the natural numbers.</p> William Chen-Mertens César Corral-Rojas Paul J. Szeptycki Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 379 389 10.4995/agt.2023.18504 Some properties defined by relative versions of star-covering properties II https://polipapers.upv.es/index.php/AGT/article/view/17926 <p>In this paper we consider some recent relative versions of Menger property called set strongly star Menger and set star Menger properties and the corresponding Hurewicz-type properties. In particular, using [2], we "easily" prove that the set strong star Menger and set strong star Hurewicz properties are between countable compactness and the property of having countable extent. Also we show that the extent of a regular set star Menger or a set star Hurewicz space cannot exceed c. Moreover, we construct (1) a consistent example of a set star Menger (set star Hurewicz) space which is not set strongly star Menger (set strongly star Hurewicz) and show that (2) the product of a set star Menger (set star Hurewicz) space with a compact space need not be set star Menger (set star Hurewicz). In particular, (1) and (2) answer some questions posed by Kočinac, Konca and Singh in [17] and [23].</p> Maddalena Bonanzinga Davide Giacopello Fortunato Maesano Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 391 405 10.4995/agt.2023.17926 Smooth fans that are endpoint rigid https://polipapers.upv.es/index.php/AGT/article/view/17922 <p>Let X be a smooth fan and denote its set of endpoints by E(X). Let E be one of the following spaces: the natural numbers, the irrational numbers, or the product of the Cantor set with the natural numbers. We prove that there is a smooth fan X such that E(X) is homeomorphic to E and for every homeomorphism h : X → X , the restriction of h to E(X) is the identity. On the other hand, we also prove that if X is any smooth fan such that E(X) is homeomorphic to complete Erdős space, then X is necessarily homeomorphic to the Lelek fan; this adds to a 1989 result by Włodzimierz Charatonik.</p> Rodrigo Hernández-Gutiérrez Logan C. Hoehn Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 407 422 10.4995/agt.2023.17922 Some topological and cardinal properties of the Nτφ-nucleus of a space X https://polipapers.upv.es/index.php/AGT/article/view/17884 <p>In this paper, we study the behavior of some topological and cardinal properties of topological spaces under the influence of the N<sub>τ</sub><sup>φ</sup> -kernel of a space X. It has been proved that the N<sub>τ</sub><sup>φ</sup>-kernel of a space X preserves the density and the network π - weight of normal spaces. Besides, shown that the N-compact kernel of a space X preserves the Souslin properties, the weight, the density, and the π -network weight of normal spaces.</p> F. G. Mukhamadiev Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 423 432 10.4995/agt.2023.17884 On e-spaces and rings of real valued e-continuous functions https://polipapers.upv.es/index.php/AGT/article/view/17743 <p>Whenever the closure of an open set is also open, it is called <em>e</em>-open and if a space have a base consisting of <em>e</em>-open sets, it is called <em>e</em>-space. In this paper we first introduce and study <em>e</em>-spaces and <em>e</em>-continuous functions (we call a function <em>f</em> from a space <em>X</em> to a space <em>Y</em> an <em>e</em>-continuous at x ∈ X if for each open set <em>V</em> containing <em>f</em>(<em>x</em>) there is an <em>e</em>-open set containing <em>x</em> with f ( U ) ⊆ V ). We observe that the quasicomponent of each point in a space <em>X</em> is determined by <em>e</em>-continuous functions on <em>X</em> and it is characterized as the largest set containing the point on which every <em>e</em>-continuous function on <em>X</em> is constant. Next, we study the rings C<sub>e</sub>( X ) of all real valued <em>e</em>-continuous functions on a space <em>X</em>. It turns out that C<sub>e</sub>( X ) coincides with the ring of real valued clopen continuous functions on <em>X</em> which is a <em>C</em>(<em>Y</em>) for a zero-dimensional space <em>Y</em> whose elements are the quasicomponents of <em>X</em>. Using this fact we characterize the real maximal ideals of C<sub>e</sub>( X ) and also give a natural representation of its maximal ideals. Finally we have shown that C<sub>e</sub>( X ) determines the topology of <em>X</em> if and only if it is a zero-dimensional space.</p> Susan Afrooz Fariborz Azarpanah Nidaah Hasan Hajee Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 433 448 10.4995/agt.2023.17743 Fixed point of Lipschitz type mappings https://polipapers.upv.es/index.php/AGT/article/view/17642 <p>In this paper, we prove some fixed point theorems for Lipschitz type mappings in the setting of metric spaces. Our results open up the unexplored area of fixed points of Lipschitz type mappings for investigation.</p> Ravindra K. Bisht Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 449 454 10.4995/agt.2023.17642 Pettis property for Polish inverse semigroups https://polipapers.upv.es/index.php/AGT/article/view/17396 <p>We study a property about Polish inverse semigroups similar to the classical theorem of Pettis about Polish groups. In contrast to what happens with Polish groups, not every Polish inverse semigroup have the Pettis property. We present several examples of Polish inverse subsemigroup of the symmetric inverse semigroup I(N) of all partial bijections between subsets of N. We also study whether our examples satisfy automatic continuity.</p> Karen Arana Jerson Pérez Carlos Uzcátegui Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 455 467 10.4995/agt.2023.17396 On φ-contractions and fixed point results in fuzzy metric spaces https://polipapers.upv.es/index.php/AGT/article/view/17130 <p><span class="fontstyle0">In this paper, </span><span class="fontstyle2">φ</span><span class="fontstyle0">-contractions are defined and then, some new fixed point theorems are established for certain nonlinear mappings associated with one-dimensional (c)-comparison functions in fuzzy metric spaces. Next, generalized </span><span class="fontstyle2">φ</span><span class="fontstyle0">-contractions are defined by using five-dimensional (c)-comparison functions, and the existence of fixed points for nonlinear maps on fuzzy metric spaces is studied. Moreover, some examples are given to illustrate our results.</span></p> Morteza Saheli Seyed Ali Mohammad Mohsenialhosseini Hadi Saeidi Goraghani Copyright (c) 2023 Applied General Topology https://creativecommons.org/licenses/by-nc-nd/4.0 2023-10-02 2023-10-02 24 2 469 483 10.4995/agt.2023.17130