Detail publikačního výsledku

On categories of ordered sets with a closure operator

ŠLAPAL, J.

Originální název

On categories of ordered sets with a closure operator

Anglický název

On categories of ordered sets with a closure operator

Druh

Článek recenzovaný mimo WoS a Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

Category, ordered set, closure operator

Klíčová slova v angličtině

Category, ordered set, closure operator

Autoři

ŠLAPAL, J.

Rok RIV

2011

Vydáno

01.01.2011

ISSN

0033-3883

Periodikum

PUBLICATIONES MATHEMATICAE DEBRECEN

Svazek

78

Číslo

1

Stát

Maďarsko

Strany od

61

Strany do

69

Strany počet

9

BibTex

@article{BUT49215,
  author="Josef {Šlapal}",
  title="On categories of ordered sets with a closure operator",
  journal="PUBLICATIONES MATHEMATICAE DEBRECEN",
  year="2011",
  volume="78",
  number="1",
  pages="61--69",
  issn="0033-3883"
}