Vol. 75, No. 1, 1978

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On coverings of Euclidean space by convex sets

Gulbank D. Chakerian and H. Groemer

Vol. 75 (1978), No. 1, 77–86
Abstract

Let 𝒦 = {K1,K2,} be an infinite countable class of compact convex subsets of euclidean n-dimensional space Rn. We shall say that 𝒦 permits a space covering or, more precisely, a covering of Rn, if there are rigid motions σ12, such that Rn i=1σiKi. In this paper we concern ourselves with necessary and sufficient conditions in order that a given class 𝒦 permits a space covering.

Mathematical Subject Classification
Primary: 52A45, 52A45
Milestones
Received: 17 August 1976
Published: 1 March 1978
Authors
Gulbank D. Chakerian
H. Groemer