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On the relation between completeness and H-closedness of pospaces without infinite antichains
Репозиторій DSpace/Manakin
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On the relation between completeness and H-closedness of pospaces without infinite antichains
Інший ID:
2010 MSC:Primary 06A06, 06F30; Secondary 54F05, 54H12.
Посилання:
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.
Підтримка:
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.
Дата:
2013
Переглядів:
466
Завантажень:
150
Анотація:
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].
