Abstract
A theorem due to Comfort and Ross asserts that the product of any family of pseudocompact topological groups is pseudocompact. We generalize this theorem to the case of Mal'tsev spaces. A Mal'tsev operation on a space X is a continuous function ƒ:X 3 → X satisfying the identity ƒ(x, y, y) = ƒ(y, y, x) = x for all x, y ϵ X. A topological space is Mal'tsev if it admits a Mal'tsev operation. We prove that every Mal'tsev operation on a pseudocompact space X can be extended to a Mal'tsev operation on βX. It follows that: 1. (1) if X is a pseudocompact Mal'tsev space, then βX is Dugundji; 2. (2) the product of any family of pseudocompact Mal'tsev spaces is pseudocompact.
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