Applied General Topology - Vol 20, No 2 (2019)
https://riunet.upv.es:443/handle/10251/127114
2020-04-07T04:26:25ZExistence results of delay and fractional differential equations via fuzzy weakly contraction mapping principle
https://riunet.upv.es:443/handle/10251/127141
Existence results of delay and fractional differential equations via fuzzy weakly contraction mapping principle
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.
2019-10-03T07:55:55ZBalleans, hyperballeans and ideals
https://riunet.upv.es:443/handle/10251/127140
Balleans, hyperballeans and ideals
Dikranjan, Dikran; Protasov, Igor; Protasova, Ksenia; Zava, Nicolò
[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.
2019-10-03T07:51:59ZOn proximal fineness of topological groups in their right uniformity
https://riunet.upv.es:443/handle/10251/127139
On proximal fineness of topological groups in their right uniformity
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.
2019-10-03T07:47:21ZMatrix characterization of multidimensional subshifts of finite type
https://riunet.upv.es:443/handle/10251/127136
Matrix characterization of multidimensional subshifts of finite type
Sharma, Puneet; Kumar, Dileep
[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.
2019-10-03T07:33:33Zec-Filters and ec-ideals in the functionally countable subalgebra of C*(X)
https://riunet.upv.es:443/handle/10251/127133
ec-Filters and ec-ideals in the functionally countable subalgebra of C*(X)
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).
2019-10-03T07:26:08ZIdeals in B1(X) and residue class rings of B1(X) modulo an ideal
https://riunet.upv.es:443/handle/10251/127130
Ideals in B1(X) and residue class rings of B1(X) modulo an ideal
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).
2019-10-03T07:21:33ZOn ideal sequence covering maps
https://riunet.upv.es:443/handle/10251/127127
On ideal sequence covering maps
Pal, Sudip Kumar; Adhikary, Nayan; Samanta, Upasana
[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].
2019-10-03T07:15:31ZRemarks on fixed point assertions in digital topology, 3
https://riunet.upv.es:443/handle/10251/127125
Remarks on fixed point assertions in digital topology, 3
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.
2019-10-03T07:10:54ZThe function ω ƒ on simple n-ods
https://riunet.upv.es:443/handle/10251/127123
The function ω ƒ on simple n-ods
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.
2019-10-03T07:05:48ZSimple dynamical systems
https://riunet.upv.es:443/handle/10251/127120
Simple dynamical systems
Ali Akbar, K.; Kannan, V.; Subramania Pillai, I.
[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.
2019-10-03T06:57:13Z