Result Details

Closure, interior and neighbourhood in a category

HOLGATE, D.; ŠLAPAL, J. Closure, interior and neighbourhood in a category. HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2018, vol. 47, no. 6, p. 1512-1520. ISSN: 1303-5010.
Type
journal article
Language
English
Authors
Holgate David, Prof.
Šlapal Josef, prof. RNDr., CSc., IM (FME)
Abstract

The natural correspondences in topology between closure, interior and neighbourhood no longer hold in an abstract categorical setting where subobject lattices are not necessarily Boolean algebras. We analyse three canonical correspondences between closure, interior and neighbourhood operators in a category endowed with a subobject structure. While these correspondences coincide in general topology, the analysis highlights subtle dierences which distinguish different approaches taken in the literature.

Keywords

Categorical closure operator, interior operator, neighbourhood operator.

URL
Published
2018
Pages
1512–1520
Journal
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, vol. 47, no. 6, ISSN 1303-5010
DOI
10.15672/HJMS.2018.628
UT WoS
000464876200010
EID Scopus
2-s2.0-85073870384
BibTeX 
@article{BUT155116,
  author="David {Holgate} and Josef {Šlapal}",
  title="Closure, interior and neighbourhood in a category",
  journal="HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS",
  year="2018",
  volume="47",
  number="6",
  pages="1512--1520",
  doi="10.15672/HJMS.2018.628",
  issn="1303-5010",
  url="http://dergipark.gov.tr/hujms/issue/41011/494828"
}
Files
Projects
IT4Innovations excellence in science, MŠMT, Národní program udržitelnosti II, LQ1602, start: 2016-01-01, end: 2020-12-31, completed
Research groups
Automated Analysis and Verification Research Group - VeriFIT (RG VERIFIT)
Departments
Faculty of Information Technology (FIT)
Back to top