Detail publikace
Connectivity with respect to α-discrete closure operators
ŠLAPAL, J.
Anglický název
Connectivity with respect to α-discrete closure operators
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
en
Originální abstrakt
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.
Anglický abstrakt
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.
Klíčová slova anglicky
closure operator, ordinal (number), ordinal-indexed sequence, connectivity, digital Jordan curve
Vydáno
01.09.2022
Nakladatel
De Gruyter
Místo
Warsaw, Poland
ISSN
2391-5455
Ročník
2022
Číslo
20
Strany od–do
682–688
Počet stran
7
BIBTEX
@article{BUT179022,
author="Josef {Šlapal},
title="Connectivity with respect to α-discrete closure operators",
year="2022",
volume="2022",
number="20",
month="September",
pages="682--688",
publisher="De Gruyter",
address="Warsaw, Poland",
issn="2391-5455"
}