Space coverings by translates of convex sets

H. Groemer

Vol. 82 (1979), No. 2, 379–386

DOI: 10.2140/pjm.1979.82.379

Abstract

Let (C_i) be a sequence of compact convex subsets of euclidean n-dimensional space Eⁿ. Some necessary and sufficient conditions in order that almost all points of Eⁿ can be covered by translates of the sets C_i are established. It is shown that such a covering is possible if and only if all points of Eⁿ can be covered by congruent copies of the sets C_i.

Mathematical Subject Classification 2000

Primary: 52A45, 52A45

Secondary: 52A20

Milestones

Received: 1 November 1978

Published: 1 June 1979