Publication result detail

Topogenous orders and closure operators on posets

ŠLAPAL, J.; RICHMOND, T.; IRAGI, M.

Original Title

Topogenous orders and closure operators on posets

English Title

Topogenous orders and closure operators on posets

Type

WoS Article

Original 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.

English 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

Key words in English

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

Authors

ŠLAPAL, J.; RICHMOND, T.; IRAGI, M.

RIV year

2025

Released

10.05.2024

Publisher

TÜBITAK

Location

Ankara

ISBN

1303-6149

Periodical

Turkish Journal of Mathematics

Volume

48

Number

3

State

Republic of Turkey

Pages from

469

Pages to

476

Pages count

8

URL

https://journals.tubitak.gov.tr/math/vol48/iss3/8/

Full text in the Digital Library

http://hdl.handle.net/11012/249517

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/"
}

Documents

Topogenous orders and closure operators on posets