Construction of a separately continuous function with given oscillation
We investigate the problem of construction of a separately continuous function f whose oscillation is equal to a given nonnegative function g. We show that, in the case of a metrizable Baire product, the problem under consideration is solvable if and only if g is upper semicontinuous and its support...
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| Date: | 1998 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4875 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511059766411264 |
|---|---|
| author | Maslyuchenko, V. K. Maslyuchenko, O. V. Маслюченко, В. К. Маслюченко, О. В. |
| author_facet | Maslyuchenko, V. K. Maslyuchenko, O. V. Маслюченко, В. К. Маслюченко, О. В. |
| author_sort | Maslyuchenko, V. K. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:16:14Z |
| description | We investigate the problem of construction of a separately continuous function f whose oscillation is equal to a given nonnegative function g. We show that, in the case of a metrizable Baire product, the problem under consideration is solvable if and only if g is upper semicontinuous and its support can be covered by countably many sets, which are locally contained in products of sets of the first category. |
| first_indexed | 2026-03-24T03:06:53Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4875 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:06:53Z |
| publishDate | 1998 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/31/83e9084bfdb30248eb322faeea98f731.pdf |
| spelling | umjimathkievua-article-48752020-03-18T21:16:14Z Construction of a separately continuous function with given oscillation Побудова нарізно неперервної функції з даним коливанням Maslyuchenko, V. K. Maslyuchenko, O. V. Маслюченко, В. К. Маслюченко, О. В. We investigate the problem of construction of a separately continuous function f whose oscillation is equal to a given nonnegative function g. We show that, in the case of a metrizable Baire product, the problem under consideration is solvable if and only if g is upper semicontinuous and its support can be covered by countably many sets, which are locally contained in products of sets of the first category. Досліджується задача побудови нарізно неперервної функції $f$, коливання якої дорівнює наперед заданій невід'ємній функції $g$. Показано, що коли добуток берівський і метризовиий, то ця задача розв'язна тоді і тільки тоді, коли $g$ напівнеперервна зверху і її носій покривається зліченним числом мпожин, що локально містяться в добутках множин першої категорії. Institute of Mathematics, NAS of Ukraine 1998-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4875 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 7 (1998); 948–959 Український математичний журнал; Том 50 № 7 (1998); 948–959 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4875/6449 https://umj.imath.kiev.ua/index.php/umj/article/view/4875/6450 Copyright (c) 1998 Maslyuchenko V. K.; Maslyuchenko O. V. |
| spellingShingle | Maslyuchenko, V. K. Maslyuchenko, O. V. Маслюченко, В. К. Маслюченко, О. В. Construction of a separately continuous function with given oscillation |
| title | Construction of a separately continuous function with given oscillation |
| title_alt | Побудова нарізно неперервної функції з даним коливанням |
| title_full | Construction of a separately continuous function with given oscillation |
| title_fullStr | Construction of a separately continuous function with given oscillation |
| title_full_unstemmed | Construction of a separately continuous function with given oscillation |
| title_short | Construction of a separately continuous function with given oscillation |
| title_sort | construction of a separately continuous function with given oscillation |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4875 |
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