Extending binary operations to funtor-spaces

Abstract

Given a continuous monadic functor $T:CompoComp$ in thecategory of compacta and a discrete topological semigroup $X$ weextend the semigroup operation $varphi:Ximes Xo X$ to aright-topological semigroup operation $Phi:Teta Ximes TetaXo Teta X,$ whose topological center $Lambda_Phi$ containsthe dense subsemigroup $T_f X$ consisting of elements $ain TetaX$ that have finite support in $X$.