Function Spaces with Uniform, Fine and Graph Topologies

McCoy, R. A.; Kundu, S.; Jindal, Varun

doi:10.1007/978-3-319-77054-3

Cited by 8 publications

(4 citation statements)

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“…In a number of subsequent results, we use the following lemma given in [28]. We include its statement here for the readers' convenience.…”

Section: Metrizability and Countability Propertiesmentioning

confidence: 99%

“…Lemma 3.1. (Lemma 1.1 on page 7, [28]) If A is a C-embedded subset of a Tychonoff space X, then any continuous function f : A → (0, ∞) can be extended to a continuous function F : X → (0, ∞). Theorem 3.2.…”

Section: Metrizability and Countability Propertiesmentioning

confidence: 99%

“…The Whitney topology has been studied in [13,17,23,25,27]. For more details on Whitney topology, we refer readers to the research monograph [28].…”

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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“…In a number of subsequent results, we use the following lemma given in [28]. We include its statement here for the readers' convenience.…”

Section: Metrizability and Countability Propertiesmentioning

confidence: 99%

Section: Metrizability and Countability Propertiesmentioning

confidence: 99%

See 1 more Smart Citation

Strong Whitney convergence on bornologies

Chauhan

Jindal

2022

Filomat

Self Cite

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“…The m-topology has been studied in detail in [1,2,4,6,7,8,11,12]. For more about u-topology and m-topology, we refer readers to the recent research monograph [13].…”

Section: Introductionmentioning

confidence: 99%