Applied General Topology - Vol 20, No 2 (2019)
Tabla de contenidos
- Simple dynamical systems
- The function ω ƒ on simple n-ods
- Remarks on fixed point assertions in digital topology, 3
- On ideal sequence covering maps
- Ideals in B1(X) and residue class rings of B1(X) modulo an ideal
- ec-Filters and ec-ideals in the functionally countable subalgebra of C*(X)
- Matrix characterization of multidimensional subshifts of finite type
- On proximal fineness of topological groups in their right uniformity
- Balleans, hyperballeans and ideals
- Existence results of delay and fractional differential equations via fuzzy weakly contraction mapping principle
URI permanente para esta colecciónhttps://riunet.upv.es/handle/10251/127114
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Item type: Artículo , Access status: Abierto , Existence results of delay and fractional differential equations via fuzzy weakly contraction mapping principle(Universitat Politècnica de València, 2019-10-01) Tabassum, Rehana; Azam, Akbar; Mohammed, Shehu Shagari[EN] The purpose of this article is to extend the results derived through former articles with respect to the notion of weak contraction into intuitionistic fuzzy weak contraction in the context of (T,N,∝) -cut set of an intuitionistic fuzzy set. We intend to prove common fixed point theorem for a pair of intuitionistic fuzzy mappings satisfying weakly contractive condition in a complete metric space which generalizes many results existing in the literature. Moreover, concrete results on existence of the solution of a delay differential equation and a system of Riemann-Liouville Cauchy type problems have been derived. In addition, we also present illustrative examples to substantiate the usability of our main result.Item type: Artículo , Access status: Abierto , Balleans, hyperballeans and ideals(Universitat Politècnica de València, 2019-10-01) Dikranjan, Dikran; Protasov, Igor; Protasova, Ksenia; Zava, Nicolò; Università degli Studi di Udine, Italia[EN] A ballean B (or a coarse structure) on a set X is a family of subsets of X called balls (or entourages of the diagonal in X × X) dened in such a way that B can be considered as the asymptotic counterpart of a uniform topological space. The aim of this paper is to study two concrete balleans dened by the ideals in the Boolean algebra of all subsets of X and their hyperballeans, with particular emphasis on their connectedness structure, more specically the number of their connected components.Item type: Artículo , Access status: Abierto , On proximal fineness of topological groups in their right uniformity(Universitat Politècnica de València, 2019-10-01) Bouziad, Ahmed[EN] A uniform space X is said to be proximally fine if every proximally continuous function defined on X into an arbitrary uniform pace Y is uniformly continuous. We supply a proof that every topological group which is functionally generated by its precompact subsets is proximally fine with respect to its right uniformity. On the other hand, we show that there are various permutation groups G on the integers N that are not proximally fine with respect to the topology generated by the sets {g ∈ G : g(A) ⊂ B}, A, B ⊂ N.Item type: Artículo , Access status: Abierto , Matrix characterization of multidimensional subshifts of finite type(Universitat Politècnica de València, 2019-10-01) Sharma, Puneet; Kumar, Dileep; National Board for Higher Mathematics[EN] Let X ⊂ AZd be a 2-dimensional subshift of finite type. We prove that any 2-dimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general d-dimensional case. We prove that the multidimensional shift space is non-empty if and only if the matrix obtained is of positive dimension. In the process, we give an alternative view of the necessary and sufficient conditions obtained for the non-emptiness of the multidimensional shift space. We also give sufficient conditions for the shift space X to exhibit periodic points.Item type: Artículo , Access status: Abierto , ec-Filters and ec-ideals in the functionally countable subalgebra of C*(X)(Universitat Politècnica de València, 2019-10-01) Veisi, Amir[EN] The purpose of this article is to study and investigate ec-filters on X and ec-ideals in C*c (X) in which they are in fact the counterparts of zc-filters on X and zc-ideals in Cc(X) respectively. We show that the maximal ideals of C*c (X) are in one-to-one correspondence with the ec-ultrafilters on X. In addition, the sets of ec-ultrafilters and zc-ultrafilters are in one-to-one correspondence. It is also shown that the sets of maximal ideals of Cc(X) and C*c (X) have the same cardinality. As another application of the new concepts, we characterized maximal ideals of C*c (X). Finally, we show that whether the space X is compact, a proper ideal I of Cc(X) is an ec-ideal if and only if it is a closed ideal in Cc(X) if and only if it is an intersection of maximal ideals of Cc(X).Item type: Artículo , Access status: Abierto , Ideals in B1(X) and residue class rings of B1(X) modulo an ideal(Universitat Politècnica de València, 2019-10-01) Deb Ray, A.; Mondal, Atanu[EN] This paper explores the duality between ideals of the ring B1(X) of all real valued Baire one functions on a topological space X and typical families of zero sets, called ZB-filters, on X. As a natural outcome of this study, it is observed that B1(X) is a Gelfand ring but non-Noetherian in general. Introducing fixed and free maximal ideals in the context of B1(X), complete descriptions of the fixed maximal ideals of both B1(X) and B1* (X) are obtained. Though free maximal ideals of B1(X) and those of B1* (X) do not show any relationship in general, their counterparts, i.e., the fixed maximal ideals obey natural relations. It is proved here that for a perfectly normal T1 space X, free maximal ideals of B1(X) are determined by a typical class of Baire one functions. In the concluding part of this paper, we study residue class ring of B1(X) modulo an ideal, with special emphasize on real and hyper real maximal ideals of B1(X).Item type: Artículo , Access status: Abierto , On ideal sequence covering maps(Universitat Politècnica de València, 2019-10-01) Pal, Sudip Kumar; Adhikary, Nayan; Samanta, Upasana; University Grants Commission, India[EN] In this paper we introduce the concept of ideal sequence covering map which is a generalization of sequence covering map, and investigate some of its properties. The present article contributes to the problem of characterization to the certain images of metric spaces which posed by Y. Tanaka [22], in more general form. The entire investigation is performed in the setting of ideal convergence extending the recent results in [11,15,16].Item type: Artículo , Access status: Abierto , Remarks on fixed point assertions in digital topology, 3(Universitat Politècnica de València, 2019-10-01) Boxer, Laurence[EN] We continue the work of [5] and [3], in which are considered papers in the literature that discuss fixed point assertions in digital topology. We discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality under "usual" conditions; or that we improve upon.Item type: Artículo , Access status: Abierto , The function ω ƒ on simple n-ods(Universitat Politècnica de València, 2019-10-01) Vidal-Escobar, Ivon; Garcia-Ferreira, Salvador[EN] Given a discrete dynamical system (X, ƒ), we consider the function ωƒ-limit set from X to 2x asωƒ(x) = {y ∈ X : there exists a sequence of positive integers n1 < n2 < … such that limk→∞ ƒnk (x) = y},for each x ∈ X. In the article [1], A. M. Bruckner and J. Ceder established several conditions which are equivalent to the continuity of the function ωƒ where ƒ: [0,1] → [0,1] is continuous surjection. It is natural to ask whether or not some results of [1] can be extended to finite graphs. In this direction, we study the function ωƒ when the phase space is a n-od simple T. We prove that if ωƒ is a continuous map, then Fix(ƒ2) and Fix(ƒ3) are connected sets. We will provide examples to show that the inverse implication fails when the phase space is a simple triod. However, we will prove that:Theorem A 2. If ƒ: T → T is a continuous function where T is a simple triod then ωƒ is a continuous set valued function iff the family {ƒ0, ƒ1, ƒ2,} is equicontinuous.As a consequence of our results concerning the ωƒ function on the simple triod, we obtain the following characterization of the unit interval.Theorem A 1. Let G be a finite graph. Then G is an arc iff for each continuous function ƒ: G → G the following conditions are equivalent: (1) The function ωƒ is continuous. (2) The set of all fixed points of ƒ2 is nonempty and connected.Item type: Artículo , Access status: Abierto , Simple dynamical systems(Universitat Politècnica de València, 2019-10-01) Ali Akbar, K.; Kannan, V.; Subramania Pillai, I.; University Grants Commission, India[EN] In this paper, we study the class of simple systems on R induced by homeomorphisms having finitely many non-ordinary points. We characterize the family of homeomorphisms on R having finitely many non-ordinary points upto (order) conjugacy. For x,y ∈ R, we say x ∼ y on a dynamical system (R,f) if x and y have same dynamical properties, which is an equivalence relation. Said precisely, x ∼ y if there exists an increasing homeomorphism h : R → R such that h ◦ f = f ◦ h and h(x) = y. An element x ∈ R is ordinary in (R,f) if its equivalence class [x] is a neighbourhood of it.