On the relation between completeness and H-closedness of pospaces without infinite antichains
We study the relation between completeness and H-closedness for topological partially ordered spaces. In general, a topological partially ordered space with an infinite antichain which is even directed complete and down-directed complete, is not H-closed. On the other hand, for a topological partial...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2013 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/152296 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the relation between completeness and H-closedness of pospaces without infinite antichains / T. Yokoyama // Algebra and Discrete Mathematics. — 2013. — Vol. 15, № 2. — С. 287–294. — Бібліогр.: 3 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862752852198293504 |
|---|---|
| author | Yokoyama, T. |
| author_facet | Yokoyama, T. |
| citation_txt | On the relation between completeness and H-closedness of pospaces without infinite antichains / T. Yokoyama // Algebra and Discrete Mathematics. — 2013. — Vol. 15, № 2. — С. 287–294. — Бібліогр.: 3 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We study the relation between completeness and H-closedness for topological partially ordered spaces. In general, a topological partially ordered space with an infinite antichain which is even directed complete and down-directed complete, is not H-closed. On the other hand, for a topological partially ordered space without infinite antichains, we give necessary and sufficient condition to be H-closed, using directed completeness and down-directed completeness. Indeed, we prove that {a pospace} X is H-closed if and only if each up-directed (resp. down-directed) subset has a supremum (resp. infimum) and, for each nonempty chain L ⊆ X, ⋁ L∈ cl ↓ L and ⋀L ∈ cl ↑ L. This extends a result of Gutik, Pagon, and Repovs [GPR].
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| first_indexed | 2025-12-07T21:18:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152296 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T21:18:55Z |
| publishDate | 2013 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Yokoyama, T. 2019-06-09T15:36:33Z 2019-06-09T15:36:33Z 2013 On the relation between completeness and H-closedness of pospaces without infinite antichains / T. Yokoyama // Algebra and Discrete Mathematics. — 2013. — Vol. 15, № 2. — С. 287–294. — Бібліогр.: 3 назв. — англ. 1726-3255 2010 MSC:Primary 06A06, 06F30; Secondary 54F05, 54H12. https://nasplib.isofts.kiev.ua/handle/123456789/152296 We study the relation between completeness and H-closedness for topological partially ordered spaces. In general, a topological partially ordered space with an infinite antichain which is even directed complete and down-directed complete, is not H-closed. On the other hand, for a topological partially ordered space without infinite antichains, we give necessary and sufficient condition to be H-closed, using directed completeness and down-directed completeness. Indeed, we prove that {a pospace} X is H-closed if and only if each up-directed (resp. down-directed) subset has a supremum (resp. infimum) and, for each nonempty chain L ⊆ X, ⋁ L∈ cl ↓ L and ⋀L ∈ cl ↑ L. This extends a result of Gutik, Pagon, and Repovs [GPR]. The author is partially supported by the JST CREST Program at Creative Research Institution, Hokkaido University. I would like to thank Professor Dušan Repovš for informing me oftheir interesting works. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the relation between completeness and H-closedness of pospaces without infinite antichains Article published earlier |
| spellingShingle | On the relation between completeness and H-closedness of pospaces without infinite antichains Yokoyama, T. |
| title | On the relation between completeness and H-closedness of pospaces without infinite antichains |
| title_full | On the relation between completeness and H-closedness of pospaces without infinite antichains |
| title_fullStr | On the relation between completeness and H-closedness of pospaces without infinite antichains |
| title_full_unstemmed | On the relation between completeness and H-closedness of pospaces without infinite antichains |
| title_short | On the relation between completeness and H-closedness of pospaces without infinite antichains |
| title_sort | on the relation between completeness and h-closedness of pospaces without infinite antichains |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152296 |
| work_keys_str_mv | AT yokoyamat ontherelationbetweencompletenessandhclosednessofpospaceswithoutinfiniteantichains |