Abstract
Let ℤ
be equipped with the Khalimsky topology κ, it is a T
-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 (ℤ
, κ). First, we prove a theorem dealing with the relationship between D-convexity and connectivity. The second result links together the convexity in ℝ
and the D-convexity in ℤ
. For this purpose, we suggest the continuous digitization of the real line segment and thus prove that the digitization of a convex subset of ℝ
is a D-convex subset of (ℤ
, κ).