Free topological groups and the projective dimension of a locally compact abelian group
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- by John Mack, Sidney A. Morris and Edward T. Ordman PDF
- Proc. Amer. Math. Soc. 40 (1973), 303-308 Request permission
Abstract:
It is shown that a free topological group on a ${k_\omega }$-space is a ${k_\omega }$-space. Using this it is proved that if $X$ is a ${k_\omega }$-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 ${k_\omega }$-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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 303-308
- MSC: Primary 22A05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0320216-6
- MathSciNet review: 0320216