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In this article we discuss classical theorems from Convex Geometry in the context of topological drawings. In a simple topological drawing of the complete graph Kn, any two edges share at most one point: either a common vertex or a point where they cross. Triangles of simple topological drawings can be viewed as convex sets, this gives a link to convex geometry.We present a generalization of Kirchberger's Theorem, a family of simple topological drawings with arbitrarily large Helly number, and a new proof of a topological generalization of Carathéodory's Theorem in the plane. We also discuss further classical theorems from Convex Geometry in the context of simple topological drawings.We introduce "generalized signotopes" as a generalization of topological drawings. As indicated by the name they are a generalization of signotopes, a structure studied in the context of encodings for arrangements of pseudolines.

Reed (1987) showed that, if two graphs are P 4-isomorphic, then either both are perfect or none of them is. In this note, we will derive an analogous result for perfect digraphs.

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