In the paper we study the preservation of pseudocompactness (respectively, countable compactness, sequential compactness, w -boundedness, totally countable compactness, countable pracompactness, sequential pseudocompactness) by Tychonoff products of pseudocompact (and countably compact) topological Brandt 0 i l -extensions of semitopological monoids with zero. In particular we show that if 0 0 ( ) ( ), :i iBl S i i B S {( t ? ) }I is a family of Hausdorff pseudocompact topological Brandt 0 i l -extensions of pseudocompact semitopological monoids with zero such that the Tychonoff product : ’{ } S i i ? I is a pseudocompact space then the direct product 0 0 ( ) ( ), :i i Bl S i i B S ’{( t ? ) }I endowed with the Tychonoff topology is a Hausdorff pseudocompact semitopological semigroup.
