| dc.date.accessioned | 2021-11-23T07:50:40Z | |
| dc.date.available | 2021-11-23T07:50:40Z | |
| dc.date.issued | 2021 | |
| dc.identifier.uri | https://archer.chnu.edu.ua/xmlui/handle/123456789/2269 | |
| dc.description.abstract | 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 $A\subseteq X$, then $A$ is the set of points of the uniform convergence for some convergent sequence $(f_n)_{n\in\omega}$ of functions $f_n:X\to \mathbb R$ if and only if $A$ is $G_\delta$-set which contains all isolated points of $X$. This result generalizes a theorem of J\'{a}n Bors\'{i}k published in 2019. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | De Gruyter | uk_UA |
| dc.relation.ispartofseries | Mathematica Slovaca; | |
| dc.relation.ispartofseries | ;71 (2) | |
| dc.subject | set of points of uniform convergence | uk_UA |
| dc.subject | uniformly Cauchy sequence | uk_UA |
| dc.title | A characterization of the uniform convergence points set of some convergent sequence of functions | uk_UA |
| dc.type | Article | uk_UA |
