The monad induced by the hom-functor in the category of topological spaces and its associated Eilenberg-Moore algebras (Q700909)

Let \(C_p: {\mathcal T}op\rightarrow{\mathcal T}op^{\text{op}}\) be the hom-like functor that associates with every topological space \(X\) the set of all continuous maps from \(X\) to the reals, supplied with the topology of pointwise convergence. Then the endofunctor \(M = C_p^{\text{op}} \circ C_p: {\mathcal T}op\rightarrow {\mathcal T}op\) naturally induces a monad on \({\mathcal T}op\). The author investigates this monad and the associated algebras.