Janiszewski's theorem
In mathematics, Janiszewski's theorem, named after the Polish mathematician Zygmunt Janiszewski, is a result concerning the topology of the plane or extended plane. It states that if "A" and "B" are closed subsets of the extended plane with connected intersection, then any two points that can be connected by paths avoiding either "A" or "B" can be connected by a path avoiding both of them. The theorem has been used as a tool for proving the Jordan curve theorem and in complex function theory.