Result Details

Topogenous orders and closure operators on posets

ŠLAPAL, J.; RICHMOND, T.; IRAGI, M. Topogenous orders and closure operators on posets. Turkish Journal of Mathematics, 2024, vol. 48, no. 3, p. 469-476. ISSN: 1303-6149.
Type
journal article
Language
English
Authors
Šlapal Josef, prof. RNDr., CSc., IM DAAG (FME)
Richmond Tom, Prof.
Iragi Minani, MSc, Ph.D.
Abstract

We introduce the notion of topogenous orders on a poset X to be certain endomaps on X. We build on
a Galois connection between endomaps and binary relations on X and study relationships between endomap properties and corresponding relational properties. In particular, we determine the topogenous orders that are in a one-to-one correspondence with (idempotent) closure operators. Extending our considerations to the categorical level, we find a cartesian closed category of topogenous systems.

Keywords

Poset, meet-complete semilattice, topogenous order, closure operator, cartesian closed category

URL
Published
2024
Pages
469–476
Journal
Turkish Journal of Mathematics, vol. 48, no. 3, ISSN 1303-6149
Publisher
TÜBITAK
Place
Ankara
DOI
10.55730/1300-0098.3519
UT WoS
001228503800008
EID Scopus
2-s2.0-85195321780
BibTeX 
@article{BUT188778,
  author="Josef {Šlapal} and Tom {Richmond} and Minani {Iragi}",
  title="Topogenous orders and closure operators on posets",
  journal="Turkish Journal of Mathematics",
  year="2024",
  volume="48",
  number="3",
  pages="469--476",
  doi="10.55730/1300-0098.3519",
  issn="1303-6149",
  url="https://journals.tubitak.gov.tr/math/vol48/iss3/8/"
}
Files
Projects
Mezinárodní mobilita výzkumníků Vysokého učení technického v Brně II, EU, OPVVV PO2 Mezinárodní mobilita výzkumných pracovníků, CZ.02.2.69/0.0/0.0/18_053/0016962, start: 2020-09-01, end: 2023-06-30, running
Departments
Institute of Mathematics (IM)
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