Publication result detail

A categorical approach to convergence

ŠLAPAL, J.

Original Title

A categorical approach to convergence

English Title

A categorical approach to convergence

Type

WoS Article

Original Abstract

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.

English abstract

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.

Keywords

Generalized net and subnet, convergence, topological category, cartesian closed category, categorical closure operator

Key words in English

Generalized net and subnet, convergence, topological category, cartesian closed category, categorical closure operator

Authors

ŠLAPAL, J.

RIV year

2017

Released

15.12.2016

Publisher

University of Niś

Location

Niś, Serbia

ISBN

0354-5180

Periodical

Filomat

Volume

30

Number

12

State

Republic of Serbia

Pages from

3329

Pages to

3338

Pages count

10

URL

http://www.doiserbia.nb.rs/img/doi/0354-5180/2016/0354-51801612329S.pdf

BibTex

@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"
}