The B-topology on S∗-doubly quasicontinuous posets
The notions of os{o}_{s}-convergence and S∗{S}^{\ast }-doubly quasicontinuous posets are introduced, which can be viewed as common generalizations of Birkhoff’s order-convergence and S∗{S}^{\ast }-doubly continuous posets, respectively. We first consider the relationship between os{o}_{s}-convergenc...
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De Gruyter
2021
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oai:doaj.org-article:cf90c26e11864a3ea26f88f36761833e2021-12-05T14:10:53ZThe B-topology on S∗-doubly quasicontinuous posets2391-545510.1515/math-2021-0035https://doaj.org/article/cf90c26e11864a3ea26f88f36761833e2021-07-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0035https://doaj.org/toc/2391-5455The notions of os{o}_{s}-convergence and S∗{S}^{\ast }-doubly quasicontinuous posets are introduced, which can be viewed as common generalizations of Birkhoff’s order-convergence and S∗{S}^{\ast }-doubly continuous posets, respectively. We first consider the relationship between os{o}_{s}-convergence and B-topology and show that the topology induced by os{o}_{s}-convergence according to the standard topological approach is the B-topology precisely. Then, the topological characterization for the S∗{S}^{\ast }-doubly quasicontinuity is presented. It is proved that a poset is S∗{S}^{\ast }-doubly quasicontinuous iff the poset equipped with the B-topology is locally hyperclosed iff the lattice of all B-open subsets of the poset is hypercontinuous. Finally, the order theoretical condition for the os{o}_{s}-convergence being topological is given and the complete regularity of B-topology on S∗{S}^{\ast }-doubly quasicontinuous posets is explored.Sun TaoLi QingguoZou ZhiweiDe Gruyterarticleos-convergenceb-topologys∗-doubly quasicontinuous poset54a2006a06MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 658-674 (2021) |
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os-convergence b-topology s∗-doubly quasicontinuous poset 54a20 06a06 Mathematics QA1-939 |
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os-convergence b-topology s∗-doubly quasicontinuous poset 54a20 06a06 Mathematics QA1-939 Sun Tao Li Qingguo Zou Zhiwei The B-topology on S∗-doubly quasicontinuous posets |
| description |
The notions of os{o}_{s}-convergence and S∗{S}^{\ast }-doubly quasicontinuous posets are introduced, which can be viewed as common generalizations of Birkhoff’s order-convergence and S∗{S}^{\ast }-doubly continuous posets, respectively. We first consider the relationship between os{o}_{s}-convergence and B-topology and show that the topology induced by os{o}_{s}-convergence according to the standard topological approach is the B-topology precisely. Then, the topological characterization for the S∗{S}^{\ast }-doubly quasicontinuity is presented. It is proved that a poset is S∗{S}^{\ast }-doubly quasicontinuous iff the poset equipped with the B-topology is locally hyperclosed iff the lattice of all B-open subsets of the poset is hypercontinuous. Finally, the order theoretical condition for the os{o}_{s}-convergence being topological is given and the complete regularity of B-topology on S∗{S}^{\ast }-doubly quasicontinuous posets is explored. |
| format |
article |
| author |
Sun Tao Li Qingguo Zou Zhiwei |
| author_facet |
Sun Tao Li Qingguo Zou Zhiwei |
| author_sort |
Sun Tao |
| title |
The B-topology on S∗-doubly quasicontinuous posets |
| title_short |
The B-topology on S∗-doubly quasicontinuous posets |
| title_full |
The B-topology on S∗-doubly quasicontinuous posets |
| title_fullStr |
The B-topology on S∗-doubly quasicontinuous posets |
| title_full_unstemmed |
The B-topology on S∗-doubly quasicontinuous posets |
| title_sort |
b-topology on s∗-doubly quasicontinuous posets |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/cf90c26e11864a3ea26f88f36761833e |
| work_keys_str_mv |
AT suntao thebtopologyonsdoublyquasicontinuousposets AT liqingguo thebtopologyonsdoublyquasicontinuousposets AT zouzhiwei thebtopologyonsdoublyquasicontinuousposets AT suntao btopologyonsdoublyquasicontinuousposets AT liqingguo btopologyonsdoublyquasicontinuousposets AT zouzhiwei btopologyonsdoublyquasicontinuousposets |
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