14 papers
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…
Residual profiles and bounded generation in pro- completions of amalgamated products
Dekui Peng, Jiang Yang
This paper completely classifies when the pro- completion of an amalgamated product has bounded generation, assuming its starting vertex groups are already boundedly generated.…
Shadowing Endomorphisms of Compact Groups
Dekui Peng
We characterize shadowing for continuous endomorphisms of compact Hausdorff groups. First, we prove that an endomorphism has shadowing if and only if its restriction to the identit…
Shadowing in Dynamical Systems: Zero-dimensional Extensions and Inverse Limits
Dekui Peng
Shifts of finite type (SFTs) play a central role in the theory of shadowing. Good and Meddaugh showed that SFTs serve as basic building blocks in the structural theory of shadowing…
Shadowing and Hyperbolicity for Endomorphisms of Locally Compact Groups
Dekui Peng
We study shadowing, with respect to the left uniformity, for continuous endomorphisms of Lie groups and totally disconnected locally compact groups. For Lie groups, an endomorphism…
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…
Remarks on -independent topological groups
Zhouxiang Huang, Dekui Peng, Gao Zhang
A non-trivial topological group is called \emph{-independent} if for every subgroup of cardinality less than the continuum there exists a countable dense subgroup intersecting i…
The Structure of Sequentially Complete Locally Minimal Groups
Dikran Dikranjan, Wei He, Dekui Peng
Generalizing results from \cite{DTk,DU} we study the fine structure of locally minimal (locally) precompact Abelian groups (these are the locally essential subgroups of LCA gro…
Density Spectra of Topological Groups
Dekui Peng, Yi Zhou
We study density spectra associated with dense and closed subgroups of topological groups. For a topological group , let $\dd^*(G)$ denote the set of densities of its dense subg…
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…
Successors of topologies of connected locally compact groups
Dekui Peng, Zhiqiang Xiao
Let be a group and be topological group topologies on . We say that is a successor of if is strictly finer than and there is not a group topology prop…
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…