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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.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…