Detail výsledku
Connectivity with respect to α-discrete closure operators
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.
closure operator, ordinal (number), ordinal-indexed sequence, connectivity, digital Jordan curve
@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"
}