Baire category properties of topological groups

Taras Banakh, Olena Hryniv


We present several known and new results on the Baire category properties in topological groups. In particular, we prove that a Baire topological group X is metrizable if and only if X is point-cosmic if and only if X is a σ-space. A topological group X is Choquet if and only if its Raikov completion X¯ is Choquet and X is Gδ-dense in X¯. A topological group X is complete-metrizable if and only if X is a point-cosmic Choquet space if and only if X is a Choquet σ-space.  Finally, we pose several open problem, in particular, whether each Choquet topological group is strong Choquet.

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