TOPOLOGICAL REASONING IN TWO DIMENSIONS

Christos Papadimitriou
Computer Sciences Division
University of California at Berkeley

Abstract

Suppose that you know the following about four simply connected regions on the plane: Region A is inside region B, B intersects C, C is disjoint from D and includes A, while region D touches A on the boundary and is disjoint from B. Is this possible? If so, we would like a model, a picture in which four simply connected regions are so related. If not, we would like a proof. This deceptively simple problem leads to many intriguing and largely unresolved research directions, including a redefinition of planarity.
Eyal Amir
Last modified: Tue Apr 28 00:40:46 PDT 1998