Strict topology on locally compact groups

Let G be a locally compact group, A a subalgebra of the measure algebra M (G), and u a family of Borel subsets of G that is closed under finite unions. In this paper, among other results, we find sufficient conditions on beta u, that imply A is a semi-topological algebra with respect to the strict topology flat. We also find necessary and sufficient conditions on G, that imply A is a topological algebra with respect to the strict topology beta u, where u is a family of Borel subsets of G with finite Haar measure. (C) 2017 Elsevier B.V. All rights reserved.