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math.GR2025
Detecting the real line among one-parametric topological groups
Taras Banakh, Kateryna Makarova, Oles Mazurenko
We prove that a topological group is isomorphic to the real line if and only if it is a one-parameteric, metrizable, and not monothetic. This result is used in the authors' other p…
math.GR2025
Locally compact strictly convex metric groups are abelian
Taras Banakh, Oles Mazurenko
We show that every locally compact strictly convex metric group is abelian, thus answering one problem posed by the authors in their earlir paper. To prove this theorem we first co…