Free Topological Groups and the Projective Dimension of a Locally Compact Abelian Group
نویسندگان
چکیده
It is shown that a free topological group on a k.space is a k.-space. Using this it is proved that if X is a k.-group then it is a quotient of a free topological group by a free topological group. A corollary to this is that the projective dimension of any k.-group, relative to the class of all continuous epimorphisms admitting sections, is either zero or one. In particular the projective dimension of a connected locally compact abelian group or a compact abelian group is exactly one.
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تاریخ انتشار 2008