Abstract
Let \U0001d53d be a monad in the category Comp of compact Hausdorff spaces and continuous maps. An abstract convexity was constructed by Radul for each \U0001d53d-algebra of the monad \U0001d53d in the category Comp. It was proved that if the convexity of the monad \U0001d53d with some additional properties is binary then \U0001d53d 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.
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