Helly Theorem and Related Results
By using the classical Helly theorem, one cannot obtain information about a family of convex compact sets in the n-dimensional Euclidean space if it is known that only subfamilies consisting of k elements, 0 < k ≤ n, have nonempty intersections. We modify the Helly theorem to fix this issue a...
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| Date: | 2002 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4045 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510174252367872 |
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| author | Zelinskii, Yu. B. Зелинский, Ю. Б. Зелинский, Ю. Б. |
| author_facet | Zelinskii, Yu. B. Зелинский, Ю. Б. Зелинский, Ю. Б. |
| author_sort | Zelinskii, Yu. B. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:20:16Z |
| description | By using the classical Helly theorem, one cannot obtain information about a family of convex compact sets in the n-dimensional Euclidean space if it is known that only subfamilies consisting of k elements, 0 < k ≤ n, have nonempty intersections. We modify the Helly theorem to fix this issue and investigate the behavior of generalized convex families. |
| first_indexed | 2026-03-24T02:52:48Z |
| format | Article |
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| id | umjimathkievua-article-4045 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:52:48Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a0/2eccafde1cae70d8f8892bbbf33c4fa0.pdf |
| spelling | umjimathkievua-article-40452020-03-18T20:20:16Z Helly Theorem and Related Results Теорема Хелли и смежные результаты Zelinskii, Yu. B. Зелинский, Ю. Б. Зелинский, Ю. Б. By using the classical Helly theorem, one cannot obtain information about a family of convex compact sets in the n-dimensional Euclidean space if it is known that only subfamilies consisting of k elements, 0 < k ≤ n, have nonempty intersections. We modify the Helly theorem to fix this issue and investigate the behavior of generalized convex families. З класичної теореми Хеллі неможна одержати інформацію про сім'ю опуклих компактів в $n$- вимірному евклідовому просторі, якщо відомо, що непусті перетини мають тільки підсім'ї, що складаються з $k$ елементів, $0 < k < n$. Уточнено теорему Хеллі для такого випадку, а також досліджено поведінку узагальнено опуклих сімей. Institute of Mathematics, NAS of Ukraine 2002-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4045 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 1 (2002); 125-128 Український математичний журнал; Том 54 № 1 (2002); 125-128 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4045/4800 https://umj.imath.kiev.ua/index.php/umj/article/view/4045/4801 Copyright (c) 2002 Zelinskii Yu. B. |
| spellingShingle | Zelinskii, Yu. B. Зелинский, Ю. Б. Зелинский, Ю. Б. Helly Theorem and Related Results |
| title | Helly Theorem and Related Results |
| title_alt | Теорема Хелли и смежные результаты |
| title_full | Helly Theorem and Related Results |
| title_fullStr | Helly Theorem and Related Results |
| title_full_unstemmed | Helly Theorem and Related Results |
| title_short | Helly Theorem and Related Results |
| title_sort | helly theorem and related results |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4045 |
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