The projective dimension of a compact abelian group

Nummela, Eric C.

doi:10.1090/S0002-9939-1973-0313362-4

The projective dimension of a compact abelian group
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by Eric C. Nummela PDF

Proc. Amer. Math. Soc. 38 (1973), 452-456 Request permission

Abstract:

Let $X$ 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 $K$ 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.

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