Absolute Extensors and Binary Monads

摘要

Let oe"1/2 be a monad in the category Comp of compact Hausdorff spaces and continuous maps. An abstract convexity was constructed by Radul for each oe"1/2 -algebra of the monad oe"1/2 in the category Comp. It was proved that if the convexity of the monad oe"1/2 with some additional properties is binary then oe"1/2 has good topological properties, in particular, FX is an absolute extensor in the class of 0-dimensional spaces for each openly generated compactum X. We show in this paper that binarity is also a necessary condition.