Quasiorders, principal topologies, and partially ordered partitions
The quasiorders on a set X are equivalent to the topologies on X which are closed under arbitrary intersections. We consider the quaisorders on X to be partial orders on the blocks of a partition of X and use this approach to survey some fundamental results on the lattice of quasiorders on X.
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000325 |
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| _version_ | 1850216637015261184 |
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| author | Thomas A. Richmond |
| author_facet | Thomas A. Richmond |
| author_sort | Thomas A. Richmond |
| collection | DOAJ |
| description | The quasiorders on a set X are equivalent to the topologies on X which are closed
under arbitrary intersections. We consider the quaisorders on X to be partial orders on the blocks
of a partition of X and use this approach to survey some fundamental results on the lattice of
quasiorders on X. |
| format | Article |
| id | doaj-art-3aec440200f740bebcceb520f60d2e32 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3aec440200f740bebcceb520f60d2e322025-08-20T02:08:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121222123410.1155/S0161171298000325Quasiorders, principal topologies, and partially ordered partitionsThomas A. Richmond0Department of Mathematics, Western Kentucky University, Bowling Green 42101, Kentucky, USAThe quasiorders on a set X are equivalent to the topologies on X which are closed under arbitrary intersections. We consider the quaisorders on X to be partial orders on the blocks of a partition of X and use this approach to survey some fundamental results on the lattice of quasiorders on X.http://dx.doi.org/10.1155/S0161171298000325Quasiorderprincipal topologypartially ordered partition specialization topologyspecialization order. |
| spellingShingle | Thomas A. Richmond Quasiorders, principal topologies, and partially ordered partitions International Journal of Mathematics and Mathematical Sciences Quasiorder principal topology partially ordered partition specialization topology specialization order. |
| title | Quasiorders, principal topologies, and partially ordered partitions |
| title_full | Quasiorders, principal topologies, and partially ordered partitions |
| title_fullStr | Quasiorders, principal topologies, and partially ordered partitions |
| title_full_unstemmed | Quasiorders, principal topologies, and partially ordered partitions |
| title_short | Quasiorders, principal topologies, and partially ordered partitions |
| title_sort | quasiorders principal topologies and partially ordered partitions |
| topic | Quasiorder principal topology partially ordered partition specialization topology specialization order. |
| url | http://dx.doi.org/10.1155/S0161171298000325 |
| work_keys_str_mv | AT thomasarichmond quasiordersprincipaltopologiesandpartiallyorderedpartitions |