On coverings of Euclidean space by convex sets

Gulbank D. Chakerian and H. Groemer

Vol. 75 (1978), No. 1, 77–86

DOI: 10.2140/pjm.1978.75.77

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 σ₁,σ₂,⋯ such that Rⁿ ⊂⋃ _i=1^∞σ_iK_i. 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