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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 452-456
- MSC: Primary 18G05; Secondary 22B05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313362-4
- MathSciNet review: 0313362