Publication result detail

Compactness and convergence with respect to a neighborhood operator

ŠLAPAL, J.

Original Title

Compactness and convergence with respect to a neighborhood operator

English Title

Compactness and convergence with respect to a neighborhood operator

Type

Peer-reviewed article not indexed in WoS or Scopus

Original Abstract

We introduce a concept of neighborhood operator on a category. Such an operator is obtained by assigning to every atom of the subobject lattice of a given object a centered stack of subobjects of the object subject to two axioms. We study separation, compactness and convergence defined in a natural way by the help of a neighborhood operator. We show that they behave analogously to the separation, compactness and convergence in topological spaces. We also investigate relationships between the separation and compactness as defined on one hand and those with respect to the closure operator induced by the neighborhood operator considered on the other hand.

English abstract

We introduce a concept of neighborhood operator on a category. Such an operator is obtained by assigning to every atom of the subobject lattice of a given object a centered stack of subobjects of the object subject to two axioms. We study separation, compactness and convergence defined in a natural way by the help of a neighborhood operator. We show that they behave analogously to the separation, compactness and convergence in topological spaces. We also investigate relationships between the separation and compactness as defined on one hand and those with respect to the closure operator induced by the neighborhood operator considered on the other hand.

Keywords

Closure and neighborhood operators on categories, separation, compactness, convergence

Key words in English

Closure and neighborhood operators on categories, separation, compactness, convergence

Authors

ŠLAPAL, J.

RIV year

2013

Released

13.04.2012

ISBN

0010-0757

Periodical

Collectanea Mathematica

Volume

63

Number

2

State

Kingdom of Spain

Pages from

123

Pages to

137

Pages count

15

BibTex

@article{BUT48576,
  author="Josef {Šlapal}",
  title="Compactness and convergence with respect to a neighborhood operator",
  journal="Collectanea Mathematica",
  year="2012",
  volume="63",
  number="2",
  pages="123--137",
  issn="0010-0757"
}