SEMIGROUP ACTIONS: PROXIMITIES, COMPACTIFICATIONS AND NORMALITY

We study equivariant compactifications of continuous actions of topological semigroups. We give a transparent description of such compactifications in terms of S-proximities, special action compatible proximities on X. This leads us to a dynamical generalization of classical Smirnov's theorem. As a strictly related concept we investigate equivariant normality of actions and give some relevant examples.