Toader Convexity in Vector Spaces

The aim of this paper is to revisit the convexity notion introduced by Toader. A part of the results are known. However, our approach brings new insight by replacing the topic into the context of segment convex structures. The main results link classical and Toader convexity and enable us to use the tools of convex and combinatorial geometry directly. As applications, we improve some earlier results and present new ones, as well.