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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| Дата: | 2013 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2013
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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
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irk-123456789-1522962019-06-11T01:25:09Z On the relation between completeness and H-closedness of pospaces without infinite antichains Yokoyama, T. 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]. 2013 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/152296 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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]. |
| format |
Article |
| author |
Yokoyama, T. |
| spellingShingle |
Yokoyama, T. On the relation between completeness and H-closedness of pospaces without infinite antichains Algebra and Discrete Mathematics |
| author_facet |
Yokoyama, T. |
| author_sort |
Yokoyama, T. |
| title |
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_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_sort |
on the relation between completeness and h-closedness of pospaces without infinite antichains |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/152296 |
| 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. |
| series |
Algebra and Discrete Mathematics |
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AT yokoyamat ontherelationbetweencompletenessandhclosednessofpospaceswithoutinfiniteantichains |
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2023-05-20T17:37:57Z |
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2023-05-20T17:37:57Z |
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1796153735623213056 |