Detail publikačního výsledku

Compactness and convergence with respect to a neighborhood operator

ŠLAPAL, J.

Originální název

Compactness and convergence with respect to a neighborhood operator

Anglický název

Compactness and convergence with respect to a neighborhood operator

Druh

Článek recenzovaný mimo WoS a Scopus

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

ŠLAPAL, J.

Rok RIV

2013

Vydáno

13.04.2012

ISSN

0010-0757

Periodikum

Collectanea Mathematica

Svazek

63

Číslo

2

Stát

Španělské království

Strany od

123

Strany do

137

Strany počet

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"
}