Applied General Topology - Vol 23, No 2 (2022)
URI permanente para esta colecciónhttps://riunet.upv.es/handle/10251/187072
Tabla de contenidos
- Dynamics of induced mappings on symmetric products, some answers
- A Urysohn lemma for regular spaces
- Partial actions of groups on hyperspaces
- On the group of homeomorphisms on R: A revisit
- The largest topological ring of functions endowed with the m-topology
- C*-algebra valued quasi metric spaces and fixed point results with an application
- Cardinal invariants and special maps of quasicontinuous functions with the topology of pointwise convergence
- On set star-Lindelöf spaces
- Results about S2-paracompactness
- Zariski topology on the spectrum of fuzzy classical primary submodules
- The Zariski topology on the graded primary spectrum of a graded module over a graded commutative ring
- Fixed point theorems for F- contraction mapping in complete rectangular M-metric space
- Fixed point theorems for a new class of nonexpansive mappings
- Fixed point results of enriched interpolative Kannan type operators with applications
- Best proximity point (pair) results via MNC in Busemann convex metric spaces
- Fredholm theory for demicompact linear relations
- Remarks on fixed point assertions in digital topology, 5
- The ε-approximated complete invariance property
- Classical solutions for the Euler equations of compressible fluid dynamics: A new topological approach
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Publicación On the group of homeomorphisms on R: A revisit(Universitat Politècnica de València, 2022-10-03) Ali Akbar, Kamaludheen; Mubeena, T.; University of Calicut; Science and Engineering Research Board, India[EN] In this article, we prove that the group of all increasing homeomorphisms on R has exactly five normal subgroups, and the group of all homeomorphisms on R has exactly four normal subgroups. There are several results known about the group of homeomorphisms on R and about the group of increasing homeomorphisms on R ([2], [6], [7] and [8]), but beyond this there is virtually nothing in the literature concerning the topological structure in the aspects of topological dynamics. In this paper, we analyze this structure in some detail.Publicación Classical solutions for the Euler equations of compressible fluid dynamics: A new topological approach(Universitat Politècnica de València, 2022-10-03) Boureni, Dalila; Georgiev, Svetlin; Kheloufi, Arezki; Mebarki, Karima; Direction Générale de la Recherche Scientifique et du Développement Technologique, Argelia[EN] In this article we study a class of Euler equations of compressible fluid dynamics. We give conditions under which the considered equations have at least one and at least two classical solutions. To prove our main results we propose a new approach based upon recent theoretical results.Publicación The ε-approximated complete invariance property(Universitat Politècnica de València, 2022-10-03) García, Gonzalo[EN] In the present paper we introduce a generalization of the complete invariance property (CIP) for metric spaces, which we will call the εapproximated complete invariance property (ε-ACIP). For our goals, we will use the so called degree of nondensifiability (DND) which, roughly speaking, measures (in the specified sense) the distance from a bounded metric space to its class of Peano continua. Our main result relates the ε-ACIP with the DND and, in particular, proves that a densifiable metric space has the ε-ACIP for each ε > 0. Also, some essentials differences between the CIP and the ε-ACIP are shown.Publicación Remarks on fixed point assertions in digital topology, 5(Universitat Politècnica de València, 2022-10-03) Boxer, Laurence[EN] As in [6, 3, 4, 5], we discuss published assertions concerning fixed points in digital metric spaces - assertions that are incorrect or incorrectly proven, or reduce to triviality.Publicación Fredholm theory for demicompact linear relations(Universitat Politècnica de València, 2022-10-03) Ammar, Aymen; Fakhfakh, Slim; Jeribi, Aref[EN] We first attempt to determine conditions on a linear relation T such that µT becomes a demicompact linear relation for each µ ∈ [0, 1) (see Theorems 2.4 and 2.5). Second, we display some results on Fredholm and upper semi-Fredholm linear relations involving a demicompact one (see Theorems 3.1 and 3.2). Finally, we provide some results in which a block matrix of linear relations becomes a demicompact block matrix of linear relations (see Theorems 4.2 and 4.3).Publicación Best proximity point (pair) results via MNC in Busemann convex metric spaces(Universitat Politècnica de València, 2022-10-03) Gabeleh, Moosa; Patle, Pradip Ramesh[EN] In this paper, we present a new class of cyclic (noncyclic) α-ψ and β-ψ condensing operators and survey the existence of best proximity points (pairs) as well as coupled best proximity points (pairs) in the setting of reflexive Busemann convex spaces. Then an application of the main existence result to study the existence of an optimal solution for a system of differential equations is demonstrated.Publicación Fixed point results of enriched interpolative Kannan type operators with applications(Universitat Politècnica de València, 2022-10-03) Abbas, Mujahid; Anjum, Rizwan; Riasat, Shakeela[EN] The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains theclasses of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskij iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an application of the main result, variational inequality problems is solved.Publicación Fixed point theorems for a new class of nonexpansive mappings(Universitat Politècnica de València, 2022-10-03) Pant, Rajendra; Shukla, Rahul[EN] We consider a new class of nonlinear mappings that generalizes two well-known classes of nonexpansive type mappings and extends some other classes of mappings. We present some existence and convergence results for this class of mappings. Some illustrative examples presented herein show the generality of the obtained results.Publicación Fixed point theorems for F- contraction mapping in complete rectangular M-metric space(Universitat Politècnica de València, 2022-10-03) Asim, Mohammad; Mujahid, Samad; Uddin, Izhar[EN] In this paper, we prove a fixed point result for F- contraction principle in the framework of rectangular M-metric space. An example is also adopted to exhibit the utility of our result. Finally, we apply our fixed point result to show the existence of solution of Fredholm integral equation.Publicación The Zariski topology on the graded primary spectrum of a graded module over a graded commutative ring(Universitat Politècnica de València, 2022-10-03) Salam, Saif; Al-Zoubi, Khaldoun[EN] Let R be a G-graded ring and M be a G-graded R-module. We define the graded primary spectrum of M, denoted by PSG(M), to be the set of all graded primary submodules Q of M such that (GrM(Q) :RM) = Gr((Q:RM)). In this paper, we define a topology on PSG(M) having the Zariski topology on the graded prime spectrum SpecG(M) as a subspace topology, and investigate several topological properties of this topological space.Publicación Zariski topology on the spectrum of fuzzy classical primary submodules(Universitat Politècnica de València, 2022-10-03) Panpho, Phakakorn; Yiarayong, Pairote; Ministry of Higher Education, Science, Research and Innovation, Tailandia[EN] Let R be a commutative ring with identity and M a unitary R-module. The fuzzy classical primary spectrum F cp.spec(M) is the collection of all fuzzy classical primary submodules A of M, the recent generalization of fuzzy primary ideals and fuzzy classical prime submodules. In this paper, we topologize FM(M) with a topology having the fuzzy primary Zariski topology on the fuzzy classical primary spectrum F cp.spec(M) as a subspace topology, and investigate the properties of this topological space.Publicación Results about S2-paracompactness(Universitat Politècnica de València, 2022-10-03) Alghamdi, Ohud; Kalantan, Lutfi[EN] We present new results regarding S2-paracompactness, that we estab-lished in [1], and its relation with other properties such as S-normality, epinormality and L-paracompactness.Publicación On set star-Lindelöf spaces(Universitat Politècnica de València, 2022-10-03) Singh, Sumit[EN] A space X is said to be set star-Lindelöf if for each nonempty subset A of X and each collection U of open sets in X such that A ⊆ SU, there is a countable subset V of U such that A ⊆ St(SV, U). The class of set star-Lindelöf spaces lie between the class of Lindel¨of spaces and the class of star-Lindelöf spaces. In this paper, we investigate the relationship between set star-Lindelöf spaces and other related spaces by providing some suitable examples and study the topological properties of set starLindelöf spaces.Publicación Cardinal invariants and special maps of quasicontinuous functions with the topology of pointwise convergence(Universitat Politècnica de València, 2022-10-03) Kumar, Mandeep; Tyagi, Brij Kishore; University Grants Commission, India[EN] For topological spaces X and Y, let Qp(X,Y) be the space of all quasicontinuous functions from X to Y with the topology of pointwise convergence. In this paper, we study the cardinal invariants such as cellularity, character, weight, density, pseudocharacter and spread of the space Qp(X,Y). We also discuss the properties of the restriction and induced maps related to the space Qp(X,Y).Publicación C*-algebra valued quasi metric spaces and fixed point results with an application(Universitat Politècnica de València, 2022-10-03) Asim, Mohammad; Kumar, Santosh; Imdad, Mohammad; George, Reny[EN] In this paper, we introduce the notion of C*-algebra valued quasi metric space to generalize the notion of C*-algebra valued metric space and investigate the topological properties besides proving some core fixed point results. Finally, we employ our one of the main results to examine the existence and uniqueness of the solution for a system of Fredholm integral equations.Publicación The largest topological ring of functions endowed with the m-topology(Universitat Politècnica de València, 2022-10-03) Chauhan, Tarun Kumar; Jindal, Varun; National Board for Higher Mathematics[EN] The purpose of this article is to identify the largest subring of the ring of all real valued functions on a Tychonoff space X, which forms a topological ring endowed with the m-topology.Publicación Partial actions of groups on hyperspaces(Universitat Politècnica de València, 2022-10-03) Martínez, Luis; Tapia, Héctor Pinedo; Ramirez, Edwar[EN] Let X be a compact Hausdorff space. In this work we translate partial actions of X to partial actions on some hyperspaces determined by X, this gives an endofunctor 2- in the category of partial actions on compact Hausdorff spaces which generates a monad in this category. Moreover, structural relations between partial actions ? on X and partial determined by 2? as well as their corresponding globalizations are established.Publicación A Urysohn lemma for regular spaces(Universitat Politècnica de València, 2022-10-03) Gupta, Ankit; Sarma, Ratna Dev[EN] Using the concept of m-open sets, M-regularity and M-normality are introduced and investigated. Both these notions are closed under arbitrary product. M-normal spaces are found to satisfy a result similar to Urysohn lemma. It is shown that closed sets can be separated by m-continuous functions in a regular space.Publicación Dynamics of induced mappings on symmetric products, some answers(Universitat Politècnica de València, 2022-10-03) Illanes, Alejandro; Martínez-de-la-Vega, Verónica; Universidad Nacional Autónoma de México; Consejo Nacional de Ciencia y Tecnología, México[EN] Let X be a metric continuum and n ∈ N. Let Fn(X) be the hyperspace of nonempty subsets of X with at most n points. If 1 ≤ m < n, we consider the quotient space Fnm(X) = Fn(X)/Fm(X). Given a mapping f : X → X, we consider the induced mappings fn : Fn(X) → Fn(X)and fnm : Fnm(X) → Fnm(X). In this paper we study relations among the dynamics of the mappings f, fn and fnm and we answer some questions, by F. Barragán, A. Santiago-Santos and J. Tenorio, related to the properties: minimality, irreducibility, strong transitivity and turbulence.