Suitable sets do not exist in certain non-separable free topological groups but do exist in linearly orderable topological groups with an ω^ω-base and in k-spaces with such bases.
Tkachenko, Generating dense subgroups of topological groups, Topol
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Suitable sets for topological groups revisited
Suitable sets do not exist in certain non-separable free topological groups but do exist in linearly orderable topological groups with an ω^ω-base and in k-spaces with such bases.