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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Main Author: Thomas A. Richmond
Format: Article
Language:English
Published: Wiley 1998-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171298000325
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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
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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