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Convexity in the Khalimsky plane

In: Mathematica Slovaca, vol. 65, no. 6
Ezzeddine Bouassida - Riyadh Gargouri - Rim Messaoud
Detaily:
Rok, strany: 2015, 1517 - 1530
Kľúčové slová:
Alexandroff space, Khalimsky topology, connectivity, digital arcs, D-convexity, Jordan curves, continuous digitization
O článku:
Let $\mathbb{Z}2$ be equipped with the Khalimsky topology $κ$, it is a $T0$-Alexandroff topology which has some specific properties concerning continuity and connectivity. We define digital-arcs and the geodesics; this enables us to define $D$-convexity on the digital plane $(\mathbb{Z}2,κ)$. First, we prove a theorem dealing with the relationship between $D$-convexity and connectivity. The second result links together the convexity in $\mathbb{R}2$ and the $D$-convexity in $\mathbb{Z}2$. For this purpose, we suggest the continuous digitization of the real line segment and thus prove that the digitization of a convex subset of $\mathbb{R}2$ is a $D$-convex subset of $(\mathbb{Z}2,κ)$.
Ako citovať:
ISO 690:
Bouassida, E., Gargouri, R., Messaoud, R. 2015. Convexity in the Khalimsky plane. In Mathematica Slovaca, vol. 65, no.6, pp. 1517-1530. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0104

APA:
Bouassida, E., Gargouri, R., Messaoud, R. (2015). Convexity in the Khalimsky plane. Mathematica Slovaca, 65(6), 1517-1530. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0104
O vydaní:
Publikované: 1. 12. 2015