On topologization of generalized Bruck-Reilly extensions

We shall give some conditions under which the topological generalized Bruck-Reilly extension admits only the direct sum topology. Also I shall prove that in the case of a topological OIP-semigroup the direct sum topology on the generalized Bruck-Reilly extension can be coarsened. Some examples of topological OIP-semigroups will be given.