8 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…
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…