Construction of Separately Continuous Functions with Given Restriction
We solve the problem of the construction of separately continuous functions on a product of two topological spaces with given restriction. It is shown, in particular, that, for an arbitrary topological space X and a function g: X → R of the first Baire class, there exists a separately continuous fun...
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| Datum: | 2003 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2003
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3947 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510080774963200 |
|---|---|
| author | Mykhailyuk, V. V. Михайлюк, В. В. |
| author_facet | Mykhailyuk, V. V. Михайлюк, В. В. |
| author_sort | Mykhailyuk, V. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:15:55Z |
| description | We solve the problem of the construction of separately continuous functions on a product of two topological spaces with given restriction. It is shown, in particular, that, for an arbitrary topological space X and a function g: X → R of the first Baire class, there exists a separately continuous function f: X × X → R such that f(x, x) = g(x) for every x ∈ X. |
| first_indexed | 2026-03-24T02:51:19Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3947 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:51:19Z |
| publishDate | 2003 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d2/cd66909a44317f6c534971028b9532d2.pdf |
| spelling | umjimathkievua-article-39472020-03-18T20:15:55Z Construction of Separately Continuous Functions with Given Restriction Побудова нарізно неперервних функцій з даним звуженням Mykhailyuk, V. V. Михайлюк, В. В. We solve the problem of the construction of separately continuous functions on a product of two topological spaces with given restriction. It is shown, in particular, that, for an arbitrary topological space X and a function g: X → R of the first Baire class, there exists a separately continuous function f: X × X → R such that f(x, x) = g(x) for every x ∈ X. Розв'язано задачу про побудову нарізно неперервних функцій на добутку двох топологічних просторів із даним звуженням. Зокрема, показано, що для довільних топологічного простору $X$ і функції $g: X → R$ першого класу Бера існує нарізно неперервна функція $f: X × X → R$ така, що $f(x, x) = g(x) $ для кожного $х є X$. Institute of Mathematics, NAS of Ukraine 2003-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3947 Ukrains’kyi Matematychnyi Zhurnal; Vol. 55 No. 5 (2003); 716-721 Український математичний журнал; Том 55 № 5 (2003); 716-721 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3947/4607 https://umj.imath.kiev.ua/index.php/umj/article/view/3947/4608 Copyright (c) 2003 Mykhailyuk V. V. |
| spellingShingle | Mykhailyuk, V. V. Михайлюк, В. В. Construction of Separately Continuous Functions with Given Restriction |
| title | Construction of Separately Continuous Functions with Given Restriction |
| title_alt | Побудова нарізно неперервних функцій з даним звуженням |
| title_full | Construction of Separately Continuous Functions with Given Restriction |
| title_fullStr | Construction of Separately Continuous Functions with Given Restriction |
| title_full_unstemmed | Construction of Separately Continuous Functions with Given Restriction |
| title_short | Construction of Separately Continuous Functions with Given Restriction |
| title_sort | construction of separately continuous functions with given restriction |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3947 |
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