Publication detail

Compactness and convergence with respect to a neighborhood operator

ŠLAPAL, J.

Czech title

Kompaktnost a konvergence vzhledem k operátoru okoli

English title

Compactness and convergence with respect to a neighborhood operator

Type

journal article - other

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.

Czech abstract

V práci je definován pojem operátoru okolí na kategorii. Tento operátor je obdržen tak, že každému atomu podobjektového svazu daného objektu je přiřazen centrovaný stack podobjektů tohoto objektu při splnění jistých axiomů. Je studována separovanost, kompaktnost a konvergence, které jsou definovány přirozeným způsobem pomocí operátora okolí.

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 in Czech

Operátory uzávěru a okolí na ketgoriích, separovanost, kompaktnost a konvergence.

Keywords in English

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

RIV year

2012

Released

13.04.2012

ISSN

0010-0757

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",
  year="2012",
  volume="63",
  number="2",
  month="April",
  pages="123--137",
  issn="0010-0757"
}