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Subgroups of -factorizable groups

Constancio Hernández, Mihail G. Tkachenko (1998)

Commentationes Mathematicae Universitatis Carolinae

The properties of -factorizable groups and their subgroups are studied. We show that a locally compact group G is -factorizable if and only if G is σ -compact. It is proved that a subgroup H of an -factorizable group G is -factorizable if and only if H is z -embedded in G . Therefore, a subgroup of an -factorizable group need not be -factorizable, and we present a method for constructing non- -factorizable dense subgroups of a special class of -factorizable groups. Finally, we construct a closed...

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