Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Peng, Dekui"'
Autor:
Peng, Dekui, Zhang, Gao
Let $\tau$ be an uncountable cardinal. The notion of a \emph{$\tau$-fine} topological group was introduced in 2021. More recently, H. Zhang et al. generalized this concept by defining pseudo-$\tau$-fine topological groups to study certain factorizati
Externí odkaz:
http://arxiv.org/abs/2412.11055
Autor:
Peng, Dekui, Xiao, Zhiqiang
Let $G$ be a group and $\sigma, \tau$ be topological group topologies on $G$. We say that $\sigma$ is a successor of $\tau$ if $\sigma$ is strictly finer than $\tau$ and there is not a group topology properly between them. In this note, we explore th
Externí odkaz:
http://arxiv.org/abs/2407.14323
Autor:
Peng, Dekui
For an infinite group $G$, the set of group topologies, $\mathcal{L}_G$, forms a complete lattice. It is known that $\mathcal{L}_G$ is modular if $G$ is abelian but the same result does not hold for nilpotent groups. We prove that the lattice $\mathc
Externí odkaz:
http://arxiv.org/abs/2310.08269
Autor:
Peng, Dekui, Shlossberg, Menachem
By [6], a minimal group $G$ is called $z$-minimal if $G/Z(G)$ is minimal. In this paper, we present the $z$-Minimality Criterion for dense subgroups with some applications to topological matrix groups. For a locally compact group $G$, let $\operatorn
Externí odkaz:
http://arxiv.org/abs/2309.17065
Autor:
Peng, Dekui
By a recent result of Juh\'{a}sz and van Mill, a locally compact topological group whose dense subspaces are all separable is metrizable. In this note we investigate the following question: is every locally compact group having all dense subgroups se
Externí odkaz:
http://arxiv.org/abs/2303.06426
Autor:
Peng, Dekui
The topological group version of the celebrated Banach-Mazur problem asks wether every infinite topological group has a non-trivial separable quotient group. It is known that compact groups have infinite separable metrizable quotient groups. However,
Externí odkaz:
http://arxiv.org/abs/2211.06831
Autor:
Peng, Dekui
In this note we show that if $G$ is a countably infinite abelian group such that $nG=0$ for some integer $n$, then the only locally minimal group topology on $G$ is the discrete one.
Externí odkaz:
http://arxiv.org/abs/1912.12764
Publikováno v:
In Topology and its Applications 1 June 2021 296
Publikováno v:
In Topology and its Applications 15 May 2021 295