Before revision:  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 Carath\'{e}odory's Theorem in the plane .
After revision:  We present a generalization of Kirchberger's Theorem that is of purely combinatorial nature. It turned out that this classical theorem also applies to "generalized signotopes" - a combinatorial generalization of simple topological drawings, which we introduce and investigate in the course of this article. As indicated by the name they are a generalization of signotopes, a structure studied in the context of encodings for arrangements of pseudolines. We also present a family of simple topological drawings with arbitrarily large Helly number, and a new proof of a topological generalization of Carath\'{e}odory's Theorem in the plane .