Pseudocompactness, Products, and Topological Brandt λ0 -Extensions of Semitopological Monoids
- Авторлар: Gutik O.V.1, Ravsky O.V.2
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Мекемелер:
- I. Franko National Lviv University
- Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences
- Шығарылым: Том 223, № 1 (2017)
- Беттер: 18-38
- Бөлім: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/239286
- DOI: https://doi.org/10.1007/s10958-017-3335-2
- ID: 239286
Дәйексөз келтіру
Аннотация
In the present 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) topological Brandt \( {\lambda}_i^0 \) -extensions of semitopological monoids with zero. In particular, we show that if \( \left\{\left({B}_{\uplambda_i}^0\left({S}_i\right),\kern0.5em {\uptau}_{B\left({S}_i\right)}^0\right):i\in \mathrm{\mathcal{I}}\right\} \) is a family of Hausdorff pseudocompact topological Brandt \( {\uplambda}_i^0 \) -extensions of pseudocompact semitopological monoids with zero such that the Tychonoff product \( \prod \left\{{S}_i:i\in \mathrm{\mathcal{I}}\right\} \) is a pseudocompact space, then the direct product \( \prod \left\{\left({B}_{\uplambda_i}^0\left({S}_i\right),\kern0.5em {\uptau}_{B\left({S}_i\right)}^0\right):i\in \mathrm{\mathcal{I}}\right\} \) endowed with the Tychonoff topology is a Hausdorff pseudocompact semitopological semigroup.
Авторлар туралы
O. Gutik
I. Franko National Lviv University
Email: Jade.Santos@springer.com
Украина, Lviv
O. Ravsky
Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences
Email: Jade.Santos@springer.com
Украина, Lviv
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