6 papers · 1 filter
The answer about Itzkowitz's Problems on FSIN groups
Dekui Peng, Li-Hong Xie, Jiang Yang
A topological group is functionally balanced if every bounded real-valued left uniformly continuous function is right uniformly continuous. We prove that every Hausdorff functional…
Countable uniformly discrete sets in functionally balanced groups
Dekui Peng, Li-Hong Xie, Jiang Yang
We prove that every countable left uniformly discrete subset of a Hausdorff functionally balanced topological group is right thin. As applications, we answer two questions of Bouzi…
Cofinal types of topological groups
Xuan Gong, Dekui Peng
We investigate the local topological structure of non-metrizable topological groups through the lens of Tukey order and cofinal types. Motivated by recent advances in topological g…
Constructing Psuedo--fine Precompact Groups
Dekui Peng, Gao Zhang
Let be an uncountable cardinal. The notion of a \emph{-fine} topological group was introduced in 2021. More recently, H. Zhang et al. generalized this concept by defining ps…
The Lattice of Group Topologies
Dekui Peng
For an infinite group , the poset of group topologies constitutes a complete lattice. Although is modular when is abelian, this property fail…
Minimality of the inner automorphism group
Dekui Peng, Menachem Shlossberg
By [6], a minimal group is called -minimal if is minimal. In this paper, we present the -Minimality Criterion for dense subgroups with some applications to topol…