Result Details
A relational generalization of the Khalimsky topology
We discuss certain n-ary relations (n > 1 an integer) and
show that each of them induces a connectedness on its underlying set.
Of these n-ary relations, we study a particular one on the digital plane Z2
for every integer n > 1. As the main result, for each of the n-ary relations
studied, we prove a digital analogue of the Jordan curve theorem for the
induced connectedness. It follows that these n-ary relations may be used
as convenient structures on the digital plane for the study of geometric
properties of digital images. For n = 2, such a structure coincides with
the (specialization order of the) Khalimsky topology and, for n > 2, it
allows for a variety of Jordan curves richer than that provided by the
Khalimsky topology.
n-ary relation, digital plane, Khalimsky topology, Jordan curve theorem
@inproceedings{BUT142992,
author="Josef {Šlapal}",
title="A relational generalization of the Khalimsky topology",
booktitle="Combinatorial Image Analysis",
year="2017",
series="Lecture Notes in Computer Sciences",
journal="Lecture Notes in Computer Science",
volume="10256",
number="10256",
pages="132--141",
publisher="Springer",
address="Switzerland",
doi="10.1007/978-3-319-59108-7\{_}11",
isbn="978-3-319-59107-0",
issn="0302-9743"
}