Publication result detail

Categorical neighborhood operators

ŠLAPAL, J.; HOLGATE, D.

Original Title

Categorical neighborhood operators

English Title

Categorical neighborhood operators

Type

Peer-reviewed article not indexed in WoS or Scopus

Original Abstract

We introduce and study a concept of neighborhood operator on a category. Such an operator is obtained by assigning a suitably axiomatized stack of subobjects -- the neighbourhoods -- to every subobject of each object in the category. We discuss closure and interior operators, convergence, separation and compactness with respect to a neighborhood operator, defined in a natural way.

English abstract

We introduce and study a concept of neighborhood operator on a category. Such an operator is obtained by assigning a suitably axiomatized stack of subobjects -- the neighbourhoods -- to every subobject of each object in the category. We discuss closure and interior operators, convergence, separation and compactness with respect to a neighborhood operator, defined in a natural way.

Keywords

Category, factorization system, closure operator, neighborhood operator, convergence, separation, compactness

Key words in English

Category, factorization system, closure operator, neighborhood operator, convergence, separation, compactness

Authors

ŠLAPAL, J.; HOLGATE, D.

RIV year

2012

Released

07.09.2011

ISBN

0166-8641

Periodical

TOPOLOGY AND ITS APPLICATIONS

Volume

158

Number

16

State

Kingdom of the Netherlands

Pages from

2356

Pages to

2365

Pages count

10

BibTex

@article{BUT73395,
  author="Josef {Šlapal} and David {Holgate}",
  title="Categorical neighborhood operators",
  journal="TOPOLOGY AND ITS APPLICATIONS",
  year="2011",
  volume="158",
  number="16",
  pages="2356--2365",
  issn="0166-8641"
}