Countably QC-Approximating Posets
As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/123762 |
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| author | Xuxin Mao Luoshan Xu |
| author_facet | Xuxin Mao Luoshan Xu |
| author_sort | Xuxin Mao |
| collection | DOAJ |
| description | As a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σcLop of all σ-Scott-closed subsets of L is weakly generalized countably approximating. |
| format | Article |
| id | doaj-art-fbdff50cc1344821b4238b37ee0f588c |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-fbdff50cc1344821b4238b37ee0f588c2025-02-03T01:23:02ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/123762123762Countably QC-Approximating PosetsXuxin Mao0Luoshan Xu1College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaDepartment of Mathematics, Yangzhou University, Yangzhou 225002, ChinaAs a generalization of countably C-approximating posets, the concept of countably QC-approximating posets is introduced. With the countably QC-approximating property, some characterizations of generalized completely distributive lattices and generalized countably approximating posets are given. The main results are as follows: (1) a complete lattice is generalized completely distributive if and only if it is countably QC-approximating and weakly generalized countably approximating; (2) a poset L having countably directed joins is generalized countably approximating if and only if the lattice σcLop of all σ-Scott-closed subsets of L is weakly generalized countably approximating.http://dx.doi.org/10.1155/2014/123762 |
| spellingShingle | Xuxin Mao Luoshan Xu Countably QC-Approximating Posets The Scientific World Journal |
| title | Countably QC-Approximating Posets |
| title_full | Countably QC-Approximating Posets |
| title_fullStr | Countably QC-Approximating Posets |
| title_full_unstemmed | Countably QC-Approximating Posets |
| title_short | Countably QC-Approximating Posets |
| title_sort | countably qc approximating posets |
| url | http://dx.doi.org/10.1155/2014/123762 |
| work_keys_str_mv | AT xuxinmao countablyqcapproximatingposets AT luoshanxu countablyqcapproximatingposets |