Extending binary operations to funtor-spaces

Keywords: functor, algebra, monad, binary operation, semigroup, right-topological semigroup, topological center
Published online: 2009-12-30

Abstract


Given a continuous monadic functor $T:\mathbf{Comp}\to\mathbf{Comp}$ in the category of compacta and a discrete topological semigroup $X$ we extend the semigroup operation $\varphi:X\times X\to X$ to a right-topological semigroup operation $\Phi:T\beta X\times T\beta X\to T\beta X,$ whose topological center $\Lambda_\Phi$ contains the dense subsemigroup $T_f X$ consisting of elements $a\in T\beta X$ that have finite support in $X$.