Prethick subsets and partitions of metric spaces
A subset $A$ of a metric space $(X,d)$ is called thick if, forevery $r>0$, there is $ain A$ such that $B_{d}(a,r)subseteqA,$ where $B_{d}(a,r)={xin Xcolon d(x,a)leq r}$. We showthat if $(X, d)$ is unbounded and has no asymptoticallyisolated balls then, for each $r>0$, there exists a partition$...
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| Format: | Article |
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Ivan Franko National University of Lviv
2012-11-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/texts/2012/38_2/115-117.pdf |
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| author | K. D. Protasova |
| author_facet | K. D. Protasova |
| author_sort | K. D. Protasova |
| collection | DOAJ |
| description | A subset $A$ of a metric space $(X,d)$ is called thick if, forevery $r>0$, there is $ain A$ such that $B_{d}(a,r)subseteqA,$ where $B_{d}(a,r)={xin Xcolon d(x,a)leq r}$. We showthat if $(X, d)$ is unbounded and has no asymptoticallyisolated balls then, for each $r>0$, there exists a partition$X=X_{1}cup X_{2}$ such that $B_{d}(X_{1},r)$ and$B_{d}(X_{2},r)$ are not thick. |
| format | Article |
| id | doaj-art-e1a11d1456554000a3bb173eb355014e |
| institution | DOAJ |
| issn | 1027-4634 |
| language | deu |
| publishDate | 2012-11-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-e1a11d1456554000a3bb173eb355014e2025-08-20T03:19:07ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342012-11-01382115117Prethick subsets and partitions of metric spacesK. D. ProtasovaA subset $A$ of a metric space $(X,d)$ is called thick if, forevery $r>0$, there is $ain A$ such that $B_{d}(a,r)subseteqA,$ where $B_{d}(a,r)={xin Xcolon d(x,a)leq r}$. We showthat if $(X, d)$ is unbounded and has no asymptoticallyisolated balls then, for each $r>0$, there exists a partition$X=X_{1}cup X_{2}$ such that $B_{d}(X_{1},r)$ and$B_{d}(X_{2},r)$ are not thick.http://matstud.org.ua/texts/2012/38_2/115-117.pdfmetric spacethick and prethick subsetsasymptotically isolated balls |
| spellingShingle | K. D. Protasova Prethick subsets and partitions of metric spaces Математичні Студії metric space thick and prethick subsets asymptotically isolated balls |
| title | Prethick subsets and partitions of metric spaces |
| title_full | Prethick subsets and partitions of metric spaces |
| title_fullStr | Prethick subsets and partitions of metric spaces |
| title_full_unstemmed | Prethick subsets and partitions of metric spaces |
| title_short | Prethick subsets and partitions of metric spaces |
| title_sort | prethick subsets and partitions of metric spaces |
| topic | metric space thick and prethick subsets asymptotically isolated balls |
| url | http://matstud.org.ua/texts/2012/38_2/115-117.pdf |
| work_keys_str_mv | AT kdprotasova prethicksubsetsandpartitionsofmetricspaces |