Swelling actions of \(\Gamma\)-compact semigroups
The authors discuss conditions which insure that an action of a topological semigroup on a Hausdorff space will allow no closed set to be swelled by a compact element of the acting semigroup. They develop and employ the concept of t-sequence along with an analog of the classical Weil lemma. Topological groups and the role of the bicyclic semigroup in swelling is also part of the discussion. A swelling \(\Gamma\)-compact action which is minimal in the sense that each \(\Gamma\)-compact action contains a subaction which has this action as a continuous homomorphic image is constructed. Moreover, this is a characterization of swelling \(\Gamma\)-compact actions. From this result it is shown that the class of \(\Gamma\)-compact c-stable (non-swelling) actions is closed under products and proper closed continuous homomorphisms.
scientific article; zbMATH DE number 3931296
scientific article