Dekui Peng

activity

20232026

collaborators

14 papers

math.GN2026

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…

math.GN2026

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…

math.GR2026

Residual profiles and bounded generation in pro- $p$ completions of amalgamated products

Dekui Peng, Jiang Yang

This paper completely classifies when the pro- $p$ completion of an amalgamated product has bounded generation, assuming its starting vertex groups are already boundedly generated.…

math.DS2026

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…

math.DS2026

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…

math.GR2026

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…

math.GN2026

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…

math.GR2026

Remarks on $d$ -independent topological groups

Zhouxiang Huang, Dekui Peng, Gao Zhang

A non-trivial topological group is called \emph{ $d$ -independent} if for every subgroup of cardinality less than the continuum there exists a countable dense subgroup intersecting i…

math.GR2025

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 $G$ of LCA gro…

math.GR2025

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 $G$ , let $\dd^*(G)$ denote the set of densities of its dense subg…

math.GN2024

Constructing Psuedo- $τ$ -fine Precompact Groups

Dekui Peng, Gao Zhang

Let $τ$ be an uncountable cardinal. The notion of a \emph{ $τ$ -fine} topological group was introduced in 2021. More recently, H. Zhang et al. generalized this concept by defining ps…

math.GR2024

Successors of topologies of connected locally compact groups

Dekui Peng, Zhiqiang Xiao

Let $G$ be a group and $σ, τ$ be topological group topologies on $G$ . We say that $σ$ is a successor of $τ$ if $σ$ is strictly finer than $τ$ and there is not a group topology prop…

math.GN2023

The Lattice of Group Topologies

Dekui Peng

For an infinite group $G$ , the poset $L_{G}$ of group topologies constitutes a complete lattice. Although $L_{G}$ is modular when $G$ is abelian, this property fail…

math.GN2023

Minimality of the inner automorphism group

Dekui Peng, Menachem Shlossberg

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 topol…

The answer about Itzkowitz's Problems on FSIN groups

Countable uniformly discrete sets in functionally balanced groups

Residual profiles and bounded generation in pro-p completions of amalgamated products

Shadowing Endomorphisms of Compact Groups

Shadowing in Dynamical Systems: Zero-dimensional Extensions and Inverse Limits

Shadowing and Hyperbolicity for Endomorphisms of Locally Compact Groups

Cofinal types of topological groups

Remarks on d-independent topological groups

The Structure of Sequentially Complete Locally Minimal Groups

Density Spectra of Topological Groups

Constructing Psuedo-τ-fine Precompact Groups

Successors of topologies of connected locally compact groups

The Lattice of Group Topologies

Minimality of the inner automorphism group

Residual profiles and bounded generation in pro- $p$ completions of amalgamated products

Remarks on $d$ -independent topological groups

Constructing Psuedo- $τ$ -fine Precompact Groups