Separately continuous functions on products of compact sets and their dependence on $\mathfrak{n}$ variables
By using the theorem on the density of the topological product and the generalized theorem on the dependence of a continuous function defined on a product of spaces on countably many coordinates, we show that every separately continuous function defined on a product of two spaces representable as pr...
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| Datum: | 1995 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1995
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5423 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511655317733376 |
|---|---|
| author | Maslyuchenko, V. K. Mykhailyuk, V. V. Маслюченко, В. К. Михайлюк, В. В. |
| author_facet | Maslyuchenko, V. K. Mykhailyuk, V. V. Маслюченко, В. К. Михайлюк, В. В. |
| author_sort | Maslyuchenko, V. K. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T08:59:05Z |
| description | By using the theorem on the density of the topological product and the generalized theorem on the dependence of a continuous function defined on a product of spaces on countably many coordinates, we show that every separately continuous function defined on a product of two spaces representable as products of compact spaces with density $≤ \mathfrak{n}$ depends on n variables. In the case of metrizable compact sets, we obtain a complete description of the sets of discontinuity points for functions of this sort. |
| first_indexed | 2026-03-24T03:16:20Z |
| format | Article |
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| id | umjimathkievua-article-5423 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:16:20Z |
| publishDate | 1995 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/31/48435136923832308cc45fb0e3344a31.pdf |
| spelling | umjimathkievua-article-54232020-03-19T08:59:05Z Separately continuous functions on products of compact sets and their dependence on $\mathfrak{n}$ variables Нарізно неперервні функції на добутках компактів і їх залежність від $\mathfrak{n}$ змінних Maslyuchenko, V. K. Mykhailyuk, V. V. Маслюченко, В. К. Михайлюк, В. В. By using the theorem on the density of the topological product and the generalized theorem on the dependence of a continuous function defined on a product of spaces on countably many coordinates, we show that every separately continuous function defined on a product of two spaces representable as products of compact spaces with density $≤ \mathfrak{n}$ depends on n variables. In the case of metrizable compact sets, we obtain a complete description of the sets of discontinuity points for functions of this sort. На основі теореми про щільність топологічного добутку і узагальнення теореми про залежність неперервної функції на добутку від зліченного числа координат показано, що кожна нарізно неперервна функція на добутку двох просторів, які є добутками компактів щільності $≤ \mathfrak{n}$, залежить від $≤ \mathfrak{n}$ змінних. У випадку метризовних компактів одержано повний опис множин точок розриву таких функцій. Institute of Mathematics, NAS of Ukraine 1995-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5423 Ukrains’kyi Matematychnyi Zhurnal; Vol. 47 No. 3 (1995); 344-350 Український математичний журнал; Том 47 № 3 (1995); 344-350 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5423/7535 https://umj.imath.kiev.ua/index.php/umj/article/view/5423/7536 Copyright (c) 1995 Maslyuchenko V. K.; Mykhailyuk V. V. |
| spellingShingle | Maslyuchenko, V. K. Mykhailyuk, V. V. Маслюченко, В. К. Михайлюк, В. В. Separately continuous functions on products of compact sets and their dependence on $\mathfrak{n}$ variables |
| title | Separately continuous functions on products of compact sets and their dependence on $\mathfrak{n}$ variables |
| title_alt | Нарізно неперервні функції на добутках компактів
і їх залежність від $\mathfrak{n}$ змінних |
| title_full | Separately continuous functions on products of compact sets and their dependence on $\mathfrak{n}$ variables |
| title_fullStr | Separately continuous functions on products of compact sets and their dependence on $\mathfrak{n}$ variables |
| title_full_unstemmed | Separately continuous functions on products of compact sets and their dependence on $\mathfrak{n}$ variables |
| title_short | Separately continuous functions on products of compact sets and their dependence on $\mathfrak{n}$ variables |
| title_sort | separately continuous functions on products of compact sets and their dependence on $\mathfrak{n}$ variables |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5423 |
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