تقرير
Joint continuity in semitopological monoids and semilattices
| العنوان: | Joint continuity in semitopological monoids and semilattices |
|---|---|
| المؤلفون: | Osipov, Alexander V., Kazachenko, Konstantin |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - General Topology, Mathematics - Group Theory, Mathematics - Rings and Algebras |
| الوصف: | In this paper we study the separately continuous actions of semitopological monoids on pseudocompact spaces. The main aim of this paper is to generalize Lawson's results to some class of pseudocompact spaces. Also, we introduce a concept of a weak $q_D$-space and prove that a pseudocompact space and a weak $q_D$-space form a Grothendieck pair. As an application of the main result, we investigate the continuity of multiplication and taking inverses in subgroups of semitopological semigroups. In particular, we get that if $(S,\bullet)$ is a Tychonoff pseudocompact semitopological monoid with a quasicontinuous multiplication $\bullet$ and $G$ is a subgroup of $S$, then $G$ is a topological group. Also, we study the continuity of operations in semitopological semilattices. Comment: 12 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.11347 |
| رقم الأكسشن: | edsarx.2309.11347 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |