On pseudocompact topological Brandt ${\lambda }^0$-extensions of semitopological monoids

Abstract

In the paper we investigate topological properties of a topological Brandt ${\lambda }^0$-extension $B_{\lambda }^0(S)$ of a semitopological monoid $S$ with zero. In particular we prove that for every Tychonoff pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) semitopological monoid $S$ with zero there exists a unique semiregular pseudocompact (resp., Hausdorff countably compact, Hausdorff compact) extension $B_{\lambda }^0(S)$ of $S$ and establish theirs Stone-Čech and Bohr compactifications. We also describe a category whose objects are ingredients in the constructions of pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt ${\lambda }^0$-extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological monoids with zeros.

Cited by in corpus (1)

• On closures in semitopological inverse semigroups with continuous inversion