Characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces
We show that a subset of the product ofn metrizable spaces is the set of discontinuity points of some separately continuous function if and only if this subset can be represented in the form of the union of a sequence ofF σ-sets each, of which is locally projectively a set of the first category.
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| Date: | 2000 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
2000
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4468 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510596354539520 |
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| 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 | 2020-03-18T20:29:37Z |
| description | We show that a subset of the product ofn metrizable spaces is the set of discontinuity points of some separately continuous function if and only if this subset can be represented in the form of the union of a sequence ofF σ-sets each, of which is locally projectively a set of the first category. |
| first_indexed | 2026-03-24T02:59:31Z |
| format | Article |
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| id | umjimathkievua-article-4468 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:59:31Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/26/0761ee48dcaa48988792e08ee04bb626.pdf |
| spelling | umjimathkievua-article-44682020-03-18T20:29:37Z Characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces Характеризація множин точок розриву нарізно неперервних функцій багатьох змінних на добутках метризовних просторів Maslyuchenko, V. K. Mykhailyuk, V. V. Маслюченко, В. К. Михайлюк, В. В. We show that a subset of the product ofn metrizable spaces is the set of discontinuity points of some separately continuous function if and only if this subset can be represented in the form of the union of a sequence ofF σ-sets each, of which is locally projectively a set of the first category. Показано, що підмножина добутку $n$ метризовних просторів є множиною точок розриву деякої нарізно неперервної функції тоді і тільки тоді, коли її можна подати у вигляді об'єднання послідовності $F_σ$-множин, які є локально проективно першої категорії. Institute of Mathematics, NAS of Ukraine 2000-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4468 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 6 (2000); 740–747 Український математичний журнал; Том 52 № 6 (2000); 740–747 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4468/5640 https://umj.imath.kiev.ua/index.php/umj/article/view/4468/5641 Copyright (c) 2000 Maslyuchenko V. K.; Mykhailyuk V. V. |
| spellingShingle | Maslyuchenko, V. K. Mykhailyuk, V. V. Маслюченко, В. К. Михайлюк, В. В. Characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces |
| title | Characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces |
| title_alt | Характеризація множин точок розриву нарізно неперервних функцій багатьох змінних на добутках метризовних просторів |
| title_full | Characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces |
| title_fullStr | Characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces |
| title_full_unstemmed | Characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces |
| title_short | Characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces |
| title_sort | characterization of the sets of discontinuity points of separately continuous functions of many variables on the products of metrizable spaces |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4468 |
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