Free Topological Groups and the Projective Dimension of a Locally Compact Abelian Group
Copyright policy )Free Topological Groups and the Projective Dimension of a Locally Compact Abelian Group
It is shown that a free topological group on a k ω {k_\omega } -space is a k ω {k_\omega } -space. Using this it is proved that if X X is a k ω {k_\omega } -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 ω {k_\omega } -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.
Structure of general topological groups, General properties and structure of locally compact groups, Projectives and injectives (category-theoretic aspects), \(k\)-spaces, General properties and structure of LCA groups
Structure of general topological groups, General properties and structure of locally compact groups, Projectives and injectives (category-theoretic aspects), \(k\)-spaces, General properties and structure of LCA groups
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