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  • We define and study two categories of partially ordered sets endowed with a closure operator. The first category has order-preserving and continuous maps as morphisms and it is shown to be concretely isomorphic to a category of ordered sets endowed with a compatible preorder. The second category studied has closed maps as morphisms and it is proved to be cartesian closed. As examples, consequences of these results for categories of the usual closure operators and, in particular, of topological spaces are discussed.
  • We define and study two categories of partially ordered sets endowed with a closure operator. The first category has order-preserving and continuous maps as morphisms and it is shown to be concretely isomorphic to a category of ordered sets endowed with a compatible preorder. The second category studied has closed maps as morphisms and it is proved to be cartesian closed. As examples, consequences of these results for categories of the usual closure operators and, in particular, of topological spaces are discussed. (en)
Title
  • On categories of ordered sets with a closure operator
  • On categories of ordered sets with a closure operator (en)
skos:prefLabel
  • On categories of ordered sets with a closure operator
  • On categories of ordered sets with a closure operator (en)
skos:notation
  • RIV/00216305:26210/11:PU80142!RIV11-MSM-26210___
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  • Z(MSM0021630518)
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  • 217979
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  • RIV/00216305:26210/11:PU80142
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  • Category, ordered set, closure operator (en)
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  • HU - Maďarsko
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  • [B2218A6A2E49]
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  • Publicationes Mathematicae Debrecen
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  • 78
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  • Šlapal, Josef
http://linked.open...n/vavai/riv/zamer
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  • 0033-3883
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  • 26210
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