Publication result detail

Closure, interior and neighbourhood in a category

HOLGATE, D.; ŠLAPAL, J.

Original Title

Closure, interior and neighbourhood in a category

English Title

Closure, interior and neighbourhood in a category

Type

WoS Article

Original 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.

English 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.

Key words in English

Categorical closure operator, interior operator, neighbourhood operator.

Authors

HOLGATE, D.; ŠLAPAL, J.

RIV year

2019

Released

14.12.2018

ISBN

1303-5010

Periodical

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS

Volume

47

Number

6

State

Republic of Turkey

Pages from

1512

Pages to

1520

Pages count

9

URL

http://dergipark.gov.tr/hujms/issue/41011/494828

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"
}

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