Remarks on sets with small differences and large sums

摘要

We use a surprising example of a subset of group Z(12) to construct the set X subset of R with int(X - X) = empty set and int(X + X) = empty set. We also build an ideal J on a compact abelian topological group G such that 3 has the closed (1,1)-Steinhaus property and does not have the closed (1, 1)-Steinhaus property. (C) 2017 Elsevier Inc. All rights reserved.