Digital Jordan Curves and Surfaces with Respect to a Closure Operator

Autor:	Josef Šlapal
Rok vydání:	2021
Předmět:	Algebra and Number Theory Computational Theory and Mathematics Mathematical analysis Closure operator Information Systems Theoretical Computer Science Mathematics
Zdroj:	Fundamenta Informaticae. 179:59-74
ISSN:	1875-8681 0169-2968
DOI:	10.3233/fi-2021-2013
Popis:	In this paper, we propose new definitions of digital Jordan curves and digital Jordan surfaces. We start with introducing and studying closure operators on a given set that are associated with n-ary relations (n > 1 an integer) on this set. Discussed are in particular the closure operators associated with certain n-ary relations on the digital line ℤ. Of these relations, we focus on a ternary one equipping the digital plane ℤ2 and the digital space ℤ3 with the closure operator associated with the direct product of two and three, respectively, copies of this ternary relation. The connectedness provided by the closure operator is shown to be suitable for defining digital curves satisfying a digital Jordan curve theorem and digital surfaces satisfying a digital Jordan surface theorem.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::d55eac5d011354d81bd05e3a7c3333e2 https://doi.org/10.3233/fi-2021-2013 Zobrazit plný text záznamu