关于拓扑幺半群的伪紧拓扑Brandt $λ^0$ -扩张
On pseudocompact topological Brandt $λ^0$-extensions of semitopological monoids
摘要：
本文研究了含零拓扑幺半群$S$的拓扑Brandt $λ^0$ -扩张$B^0_λ(S)$的拓扑性质.特别地，我们证明了对于每一个Tychonoff伪紧（分别为，Hausdorff可数紧的，Hausdorff紧的）半正则幺半群$S$存在唯一的半正则伪紧的（分别是，Hausdorff可数紧的，Hausdorff紧的）$S$的扩张$B^0_λ(S)$，并建立了它们的Stone-Čech和Bohr紧化.我们还描述了一个范畴，它的对象是伪紧（分别为，可数紧的，序列紧的，紧的）拓扑Brandt $λ^0$ -伪紧的扩展（分别，可数紧的，序列紧的，紧的）带零的拓扑幺半群。
英文摘要：
In the paper we investigate topological properties of a topological Brandt $λ^0$-extension $B^0_λ(S)$ 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 $B^0_λ(S)$ 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 $λ^0$-extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological monoids with zeros.
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