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arXiv · 1510.05096

Pseudocompactness, products and topological Brandt $λ^0$-extensions of semitopological monoids

Oleg Gutik·Oleksandr Ravsky
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Abstract

In the paper we study the preservation of pseudocompactness (resp., countable compactness, sequential compactness, $ω$-boundedness, totally countable compactness, countable pracompactness, sequential pseudocompactness) by Tychonoff products of pseudocompact (and countably compact) to\-pological Brandt $λ_i^0$-extensions of semitopological monoids with zero. In particular we show that if $\big\{ \big(B^0_{λ_i}(S_i),τ^0_{B(S_i)}\big) \colon i\in\mathscr{I}\big\}$ is a family of Hausdorff pseudocompact to\-pological Brandt $λ_i^0$-extensions of pseudocompact semitopological monoids with zero such that the Tychonoff product $\prod\left\{ S_i \colon i\in\mathscr{I}\right\}$ is a pseudocompact space then the direct product $\prod\big\{ \big(B^0_{λ_i}(S_i),τ^0_{B(S_i)}\big) \colon i\in\mathscr{I}\big\}$ endowed with the Tychonoff topology is a Hausdorff pseudocompact semitopological semigroup.

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BibTeXRIS

Oleg Gutik, Oleksandr Ravsky. 2015-10-17. Pseudocompactness, products and topological Brandt $λ^0$-extensions of semitopological monoids. https://arxiv.org/abs/1510.05096

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