Publication detail

Compactness and convergence with respect to a neighborhood operator

ŠLAPAL, J.

English title

Compactness and convergence with respect to a neighborhood operator

Type

Peer-reviewed article not indexed in WoS or Scopus

Language

en

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.

Keywords in English

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

Released

2012-04-13

ISSN

0010-0757

Journal

Collectanea Mathematica

Volume

63

Number

2

Pages from–to

123–137

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"
}