Publication result detail

Connectivity with respect to α-discrete closure operators

ŠLAPAL, J.

Original Title

Connectivity with respect to α-discrete closure operators

English Title

Connectivity with respect to α-discrete closure operators

Type

WoS Article

Original Abstract

We discuss certain closure operators that generalize the Alexandroff topologies. Such a closure operator is defined for every ordinal α > 0 in such a way that the closure of a set A is given by closures of certain α-indexed sequences formed by points of A. It is shown that connectivity with respect to such a closure operator can be viewed as a special type of path connectivity. This makes it possible to apply the operators in solving problems based on employing a convenient connectivity such as problems of digital image processing. One such application is presented providing a digital analogue of the Jordan curve theorem.

English abstract

We discuss certain closure operators that generalize the Alexandroff topologies. Such a closure operator is defined for every ordinal α > 0 in such a way that the closure of a set A is given by closures of certain α-indexed sequences formed by points of A. It is shown that connectivity with respect to such a closure operator can be viewed as a special type of path connectivity. This makes it possible to apply the operators in solving problems based on employing a convenient connectivity such as problems of digital image processing. One such application is presented providing a digital analogue of the Jordan curve theorem.

Keywords

closure operator, ordinal (number), ordinal-indexed sequence, connectivity, digital Jordan curve

Key words in English

closure operator, ordinal (number), ordinal-indexed sequence, connectivity, digital Jordan curve

Authors

ŠLAPAL, J.

RIV year

2023

Released

01.09.2022

Publisher

De Gruyter

Location

Warsaw, Poland

ISBN

2391-5455

Periodical

Open Mathematics

Volume

2022

Number

20

State

Republic of Poland

Pages from

682

Pages to

688

Pages count

7

URL

https://www.degruyter.com/document/doi/10.1515/math-2022-0046/html

BibTex

@article{BUT179022,
  author="Josef {Šlapal}",
  title="Connectivity with respect to α-discrete closure operators",
  journal="Open Mathematics",
  year="2022",
  volume="2022",
  number="20",
  pages="682--688",
  doi="10.1515/math-2022-0046",
  issn="2391-5455",
  url="https://www.degruyter.com/document/doi/10.1515/math-2022-0046/html"
}