Publication result detail

On categories of ordered sets with a closure operator

ŠLAPAL, J.

Original Title

On categories of ordered sets with a closure operator

English Title

On categories of ordered sets with a closure operator

Type

Peer-reviewed article not indexed in WoS or Scopus

Original Abstract

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.

English abstract

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.

Keywords

Category, ordered set, closure operator

Key words in English

Category, ordered set, closure operator

Authors

ŠLAPAL, J.

RIV year

2011

Released

01.01.2011

ISBN

0033-3883

Periodical

PUBLICATIONES MATHEMATICAE DEBRECEN

Volume

78

Number

1

State

Hungary

Pages from

61

Pages to

69

Pages count

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"
}