اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe Rees-Suschkewitsch Theorem for simple topological semigroups
228
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product of a topological group over topological spaces with a continuous sandwich function. We prove that a simple topological semigroup $S$ is a topological paragroup if one of the following conditions is satisfied: (1) $S$ is completely simple and the maximal subgroups of $S$ are topological groups, (2) $S$ contains an idempotent and the square $Stimes S$ is countably compact or pseudocompact, (3) $S$ is sequentially compact or each power of $S$ is countably compact. The last item generalizes an old Wallaces result saying that each simple compact topological semigroup is a topological paragroup.
قيم البحث
اقرأ أيضاً
We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that each topological semigroup S with pseudocompact square contains no dense copy of C(p,q). On the other hand, we c
onstruct a (consistent) example of a pseudocompact (countably compact) Tychonov semigroup containing a copy of C(p,q).
We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its the Stone-v{C}ech compactification $beta S$ provided $S$ is a pseudocompact openly factorizable space, which means that each map $
f:Sto Y$ to a second countable space $Y$ can be written as the composition $f=gcirc p$ of an open map $p:Xto Z$ onto a second countable space $Z$ and a map $g:Zto Y$. We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.
The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spacial. A special class o
f spacial fibrous preorders consisting of an interconnected family of preorders indexed by a unitary magma is called cartesian and studied here. Topological spaces that are obtained from those fibrous preorders, with a unitary magma emph{I}, are called emph{I}-cartesian and characterized. The characterization reveals a hidden structure of such spaces. Several other characterizations are obtained and special attention is drawn to the case of a monoid equipped with a topology. A wide range of examples is provided, as well as general procedures to obtain topologies from other data types such as groups and their actions. Metric spaces and normed spaces are considered as well.
A topological group $X$ is called $duoseparable$ if there exists a countable set $Ssubseteq X$ such that $SUS=X$ for any neighborhood $Usubseteq X$ of the unit. We construct a functor $F$ assigning to each (abelian) topological group $X$ a duoseparab
le (abelain-by-cyclic) topological group $FX$, containing an isomorphic copy of $X$. In fact, the functor $F$ is defined on the category of unital topologized magmas. Also we prove that each $sigma$-compact locally compact abelian topological group embeds into a duoseparable locally compact abelian-by-countable topological group.
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 $G$.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
