pseudocompact

— In particular we show that if #92;big#92;#123;#92;big(B⁰#95;#123;#92;lambda#95;i#125;(S#95;i),#92;tau⁰#95;#123;B(S#95;i)#125;#92;big)#92;coloni#92;in#92;mathcal#123;I#125;#92;big#92;#125; is a family of Hausdorff pseudocompact to\-pological Brandt #92;lambda#95;i⁰-extensions of pseudocompact semitopological monoids with zero such that the Tychonoff product #92;prod#92;left#92;#123;S#95;i#92;coloni#92;in#92;mathcal#123;I#125;#92;right#92;#125; is a pseudocompact space then the direct product #92;prod#92;big#92;#123;#92;big(B⁰#95;#123;#92;lambda#95;i#125;(S#95;i),#92;tau⁰#95;#123;B(S#95;i)#125;#92;big)#92;coloni#92;in#92;mathcal#123;I#125;#92;big#92;#125; endowed with the Tychonoff topology is a Hausdorff pseudocompact semitopological semigroup..