Vol. 53, No. 1, 1974

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Decomposition theorems for 3-convex subsets of the plane

Marilyn Breen

Vol. 53 (1974), No. 1, 43–57
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
Authors
Marilyn Breen