Partitioning ℝⁿ into Connected Components

Abstract

Intuition is one of the crucial parts in mathematical research. However, it might turn out to be a deceiving part. Statements that seem to be obvious are very hard to prove or they are even not valid. In this note we describe an example that has both features. Although it is “obvious,” its proof in ℝ² is based on a deep result and it is not true in ℝ³.