Points of uniform convergence and quasicontinuity

Borsík, Ján

doi:10.1007/s40879-018-0303-4

Cited by 3 publications

(3 citation statements)

References 13 publications

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“…Since X is perfectly normal, for every n ∈ N there exist continuous functions 1] defined by the formula α n = ϕ n − ψ n has the following properties:…”

Section: Proof Of Theoremmentioning

confidence: 99%

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A characterization of the uniform convergence points set of some convergent sequence of functions

Karlova¹

2020

Preprint

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We characterize the uniform convergence points set of a pointwisely convergent sequence of real-valued functions defined on a perfectly normal space. We prove that if X is a perfectly normal space which can be covered by a disjoint sequence of dense subsets and A ⊆ X, then A is the set of points of the uniform convergence for some convergent sequence (fn)n∈ω of functions fn : X → R if and only if A is G δ -set which contains all isolated points of X. This result generalizes a theorem of Ján Borsík published in 2019.

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“…Since X is perfectly normal, for every n ∈ N there exist continuous functions 1] defined by the formula α n = ϕ n − ψ n has the following properties:…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…After appearance of this theorem many results were obtained in similar directions: other types of convergence and other classes of functions were considered (see, for instance, [1,4,7,8,9,10,12,13,14]). Ján Borsík studied in [1], in particular, the uniform convergence points set of a (convergent pointwisely) sequence of functions.…”

Section: Introductionmentioning

confidence: 99%

A characterization of the uniform convergence points set of some convergent sequence of functions

Karlova¹

2020

Preprint

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“…Works [45,48,50,51] In his last paper [52], Points of uniform convergence and quasicontinuity, which appeared in European Journal of Mathematics in 2019, sets of points of uniform convergence for sequences of quasicontinuous functions and for convergent sequences of functions are characterized. It is proved that a subset of a metric space is the set of points of uniform convergence for some convergent sequence of functions if and only if it is a G δ -set containing all isolated points.…”

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confidence: 99%

Ján Borsík (1955 – 2019)

Frič

Holá²

2019

Tatra Mountains Mathematical Publications

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The sad news reached the participants of the 33rd International Summer Conference on Real Functions held in Ustka, Poland, only three days later. True, Ján struggled with cancer over a longer period, however, was still an active member of the "real functions community". Exactly one year ago, he headed/managed the 32nd ISCRF in Stará Lesná and served as an editor of the present issue of Tatra Mountains Mathematical Publications. True, the treacherous illness severely limited his life and he had to step down from his teaching duties and editorial responsibilities in last months. Even though the participants of the 33rd ISCRF could not participate in his funeral, they expressed their deep sorrow, and during the conference commemorated Professor Ján Borsík, his personal and research qualities, friendship and services to the conferrence. It is only natural to devote the present issue of TMMP to his memory. Ján Borsík was born on 11. 9. 1955 in Trstené, Slovakia. After completing his secondary education, in the period 1975-1980 he studied at the School of Natural Sciences, Comenius University in Bratislava, Slovakia. Already as a student, he participated in a scientific seminar devoted to real functions led by Professor TiborŠalát and remained faithful to real functions all his life. After his graduation, Janko Borsík obtained his RNDr. title in 1981 and, under the supervision of ProfessorŠalát, the scientific degree CSc. (equivalent to PhD). Finally, based on his Habilitationshrift, in 1999 he was promoted to Docent in Mathematics. Since 1980 until his premature death, he was affiliated with the Mathematical Institute of Slovak Academy of Sciences, Extension in Košice, as a Senior Scientific Fellow. For a long time Professor Ján Borsík lectured at theŠafárik University and the Technical University in Košice and at the Prešov University in Prešov, where his colleagues and students appreciated his scientific and pedagogical masterships very much. The same can be said about several PhD students and members of the broader Slovak mathematical community.

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A characterization of the uniform convergence points set of some convergent sequence of functions

Karlova

2021

Mathematica Slovaca

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We characterize the uniform convergence points set of a pointwisely convergent sequence of real-valued functions defined on a perfectly normal space. We prove that if X is a perfectly normal space which can be covered by a disjoint sequence of dense subsets and A ⊆ X, then A is the set of points of the uniform convergence for some convergent sequence (fn ) n∈ω of functions fn : X → ℝ if and only if A is Gδ -set which contains all isolated points of X. This result generalizes a theorem of Ján Borsík published in 2019.

show abstract

Points of uniform convergence and quasicontinuity

Cited by 3 publications

References 13 publications

A characterization of the uniform convergence points set of some convergent sequence of functions

A characterization of the uniform convergence points set of some convergent sequence of functions

Ján Borsík (1955 – 2019)

A characterization of the uniform convergence points set of some convergent sequence of functions

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