Result Details
On categories of ordered sets with a closure operator
ŠLAPAL, J. On categories of ordered sets with a closure operator. PUBLICATIONES MATHEMATICAE DEBRECEN, 2011, vol. 78, no. 1, p. 61-69. ISSN: 0033-3883.
Type
journal article
Language
English
Authors
Šlapal Josef, prof. RNDr., CSc., IM (FME)
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
Published
2011
Pages
61–69
Journal
PUBLICATIONES MATHEMATICAE DEBRECEN, vol. 78, no. 1, ISSN 0033-3883
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"
}
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