Detail výsledku
Compactness and convergence with respect to a neighborhood operator
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.
Closure and neighborhood operators on categories, separation, compactness, convergence
@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"
}