# 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