ترغب بنشر مسار تعليمي؟ اضغط هنا

Suitable sets for strongly topological gyrogroups

57   0   0.0 ( 0 )
 نشر من قبل Fucai Lin
 تاريخ النشر 2020
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

A discrete subset $S$ of a topological gyrogroup $G$ with the identity $0$ is said to be a {it suitable set} for $G$ if it generates a dense subgyrogroup of $G$ and $Scup {0}$ is closed in $G$. In this paper, it was proved that each countable Hausdorff topological gyrogroup has a suitable set; moreover, it is shown that each separable metrizable strongly topological gyrogroup has a suitable set.



قيم البحث

اقرأ أيضاً

66 - Meng Bao , Fucai Lin 2019
Topological gyrogroups, with a weaker algebraic structure than groups, have been investigated recently. In this paper, we prove that every feathered strongly topological gyrogroup is paracompact, which implies that every feathered strongly topologica l gyrogroup is a $D$-space and gives partial answers to two questions posed by A.V.Arhangel skivi ~(2010) in cite{AA1}. Moreover, we prove that every locally compact $NSS$-gyrogroup is first-countable. Finally, we prove that each Lindel{o}f $P$-gyrogroup is Ra$check{imath}$kov complete.
107 - Yingying Jin , Li-Hong Xie 2021
The concept of gyrogroups is a generalization of groups which do not explicitly have associativity. Recently, Atiponrat extended the idea of topological (paratopological) groups to topological (paratopological) gyrogroups. In this paper, we prove tha t every regular (Hausdorff) locally gyroscopic invariant paratopological gyrogroup $G$ is completely regular (function Hausdorff). These results improve theorems of Banakh and Ravsky for paratopological groups. Also, we extend the Pontrjagin conditions of (para)topological groups to (para)topological gyrogroups.
149 - Meng Bao , Fucai Lin 2020
Topological gyrogroups, with a weaker algebraic structure without associative law, have been investigated recently. We prove that each $T_{0}$-strongly topological gyrogroup is completely regular. We also prove that every $T_{0}$-strongly topological gyrogroup with a countable pseudocharacter is submetrizable. Finally, we prove that the left coset space $G/H$ is submetrizable if $H$ is an admissible $L$-subgyrogroup of a $T_{0}$-strongly topological gyrogroup $G$.
100 - Meng Bao , Xiaoyuan Zhang , 2020
Separability is one of the most basic and important topological properties. In this paper, the separability in (strongly) topological gyrogroups is studied. It is proved that every first-countable left {omega}-narrow strongly topological gyrogroup is separable. Furthermore, it is shown that if a feathered strongly topological gyrogroup G is isomorphic to a subgyrogroup of a separable strongly topological gyrogroup, then G is separable. Therefore, if a metrizable strongly topological gyrogroup G is isomorphic to a subgyrogroup of a separable strongly topological gyrogroup, then G is separable, and if a locally compact strongly topological gyrogroup G is isomorphic to a subgyrogroup of a separable strongly topological gyrogroup, then G is separable.
125 - Meng Bao , Fucai Lin 2020
A space $X$ is submaximal if any dense subset of $X$ is open. In this paper, we prove that every submaximal topological gyrogroup of non-measurable cardinality is strongly $sigma$-discrete. Moreover, we prove that every submaximal strongly topologica l gyrogroup of non-measurable cardinality is hereditarily paracompact.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا