Products of Locally Compact Groups with Zero and Their Actions

In [4], Hofmann defines a locally compact group with zero as a Hausdorff locally compact topological semigroup, S, with a non-isolated point, 0, such that G = S — {0} is a group. He shows there that 0 is indeed a zero for 5, G is a locally compact topological group, and the identity of G is the identity of S. The author has investigated actions of such semigroups on locally compact spaces in [1; 2]. In this paper, we are investigating direct products of semigroups of the above type and actions of these products; for a special case of this, the reader is referred to [3].