Decomposition theorems for 3-convex subsets of the plane

Marilyn Breen

Vol. 53 (1974), No. 1, 43–57

DOI: 10.2140/pjm.1974.53.43

Abstract

Let S be a 3-convex subset of the plane. If (clS ∼ S) ⊆ int (cl S) or if (clS ∼ S) ⊆ bdry (cl S), then S is expressible as a union of four or fewer convex sets. Otherwise, S is a union of six or fewer convex sets. In each case, the bound is best possible.

Mathematical Subject Classification 2000

Primary: 52A10

Milestones

Received: 15 May 1973

Published: 1 July 1974