### Extending binary operations to funtor-spaces

#### 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 $X$.

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