Strong Whitney and strong uniform convergences on a bornology

Chauhan, Tarun Kumar; Jindal, Varun

doi:10.1016/j.jmaa.2021.125634

Cited by 5 publications

(6 citation statements)

References 31 publications

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“…The relationships between the above mentioned topologies are thoroughly studied in [12]. The following result proved in [12], we need in the sequel.…”

Section: Preliminariesmentioning

confidence: 98%

“…The relationships between the above mentioned topologies are thoroughly studied in [12]. The following result proved in [12], we need in the sequel. Note that for a bornology B on a metric space (X, d) with a closed base, B ⊆ K if and only if B has a compact base.…”

Section: Preliminariesmentioning

confidence: 98%

“…The properties of the spaces (C(X), τ w B ) and (C(X), τ sw B ) are yet to be explored in detail. Recently, τ w Bconvergence and τ sw B -convergence have been studied in [12]. The main objective of this paper is to characterize the metrizability and various countability properties of C(X) equipped with the topologies τ w B and τ sw B .…”

Section: Introductionmentioning

confidence: 99%

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Strong Whitney convergence on bornologies

Chauhan

Jindal

2022

Filomat

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The strong Whitney convergence on bornology introduced by Caserta in [9] is a generalization of the strong uniform convergence on bornology introduced by Beer-Levi in [5]. This paper aims to study some important topological properties of the space of all real valued continuous functions on a metric space endowed with the topologies of Whitney and strong Whitney convergence on bornology. More precisely, we investigate metrizability, various countability properties, countable tightness, and Fr?chet property of these spaces. In the process, we also present a new characterization for a bornology to be shielded from closed sets.

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“…The relationships between the above mentioned topologies are thoroughly studied in [12]. The following result proved in [12], we need in the sequel.…”

Section: Preliminariesmentioning

confidence: 98%

Section: Preliminariesmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Strong Whitney convergence on bornologies

Chauhan

Jindal

2022

Filomat

Self Cite

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“…Therefore, strongly uniform convergence dynamical system has attracted great attention of scholars at home and abroad. The research results can be found in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. For example, Ji [1] proved that if sequence maps 1 { } n n f f are strongly uniform converge to the map f where f is equicontinuous, then we can get that limsup ( ) ( )…”

Section: Introductionmentioning

confidence: 99%

Topological Structure of QWG(f) Set

Bei

2022

Advances in Transdisciplinary Engineering

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According to the definition of quasiweak almost periodic point, we introduce the definition of QWG(f) in the paper. We studied topological structure of G-quasiweak almost periodic point set. We have the following two results: (1) Let (Y,d′) be a compact G–metric space and f : X → X be equicontinuous. Let {fn}∞n=1 be G-strongly uniform converge to the map f and xk ∈ QWG(fn). If limk → ∞ xk = x, then x ∈ QWG(f); (2) Let (Y,d′) be a compact G-metric space and f : X → X be equicontinuous. If {fn}∞n=1 is G-strongly uniform converge to f, then we have lim sup QWG(fn) ⊂ QWG(f). The conclusions results generalize the corresponding results given in [Journal of Southwest China Normal University: Natural Science Edition 44(2019), 40-44].

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“…The research results of strongly uniform convergence are shown in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For example, Ji and Zhang [1] proved that if sequence map…”

Section: Introductionmentioning

confidence: 99%

The Research of G-Almost Periodic Point

Bei

2022

Advances in Transdisciplinary Engineering

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Firstly, it is introduced that the concepts of G-almost periodic point and G-sequence shadowing property. Then, we discuss the dynamical relationship between sequence map {gk}∞k=1 and limit map g under G-strongly uniform convergence of topological group action. We can get that (1) Let sequence map {gk}∞k=1 be G-strongly uniform converge to the map g where g is equicontinuous and the point sequence {yk}∞k=1 be the G-almost periodic point of sequence map {gk}∞k=1. If limk → ∞ yk = y, then the point y is an G-almost periodic point of the map g; (2) If sequence map {gk}∞k=1 are G-strongly uniform converge to the map g where g is equicontinuous, then limsup APG(gk) ⊂ APG(g); (3) Let sequence map {gk}∞k=1 be G-strongly uniform converge to the map g. If every map gk has G-fine sequence shadowing property, the map g has G-sequence shadowing property. These results generalize the corresponding results given in Ji and Zhang [1] and make up for the lack of theory under G-strongly uniform convergence of group action.

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Strong Whitney and strong uniform convergences on a bornology

Cited by 5 publications

References 31 publications

Strong Whitney convergence on bornologies

Strong Whitney convergence on bornologies

Topological Structure of QWG(f) Set

The Research of G-Almost Periodic Point

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