Detail výsledku
A categorical approach to convergence
We define the concept of a convergence classes on an object of a given category by using certain generalized nets for expressing the convergence. The resulting topological category, whose objects are the pairs consisting of objects of the original category and convergence classes on them, is then investigated. We study full subcategories of this category which are obtained by imposing some natural convergence axioms. In particular, we find sufficient conditions for the subcategories to be cartesian closed. We also investigate behavior of the closure operators associated with the convergence in a natural way.
Generalized net and subnet, convergence, topological category, cartesian closed category, categorical closure operator
@article{BUT113319,
author="Josef {Šlapal}",
title="A categorical approach to convergence",
journal="Filomat",
year="2016",
volume="30",
number="12",
pages="3329--3338",
doi="10.2298/FIL1612329S",
issn="0354-5180",
url="http://www.doiserbia.nb.rs/img/doi/0354-5180/2016/0354-51801612329S.pdf"
}