Vol. 82, No. 2, 1979

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Space coverings by translates of convex sets

H. Groemer

Vol. 82 (1979), No. 2, 379–386
Abstract

Let (Ci) 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 Ci 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 Ci.

Mathematical Subject Classification 2000
Primary: 52A45, 52A45
Secondary: 52A20
Milestones
Received: 1 November 1978
Published: 1 June 1979
Authors
H. Groemer