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The Projective Dimension of a Compact Abelian Group

1973
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Proceedings of the American Mathematical Society
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Let A" be a compact group, FGX the (Graev) free topological group generated by X, and K the kernel of the canonical quotient morphism from FGX to X. Then A" is a (Graev) free topological group. A corollary to the abelian analogue of this theorem is that the projective dimension of a compact abelian group, relative to the class of all continuous epimorphisms admitting sections, is exactly one. Introduction. Let 'S (respectively, s/) denote the category of topological (abelian) groups and

doi:10.2307/2038930
fatcat:i7bdkjg525cfveiogm5fk22cvm