Free topological groups and the projective dimension of a locally compact abelian group

Authors:
John Mack, Sidney A. Morris and Edward T. Ordman

Journal:
Proc. Amer. Math. Soc. **40** (1973), 303-308

MSC:
Primary 22A05

MathSciNet review:
0320216

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Abstract: It is shown that a free topological group on a -space is a -space. Using this it is proved that if is a -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 -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.

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DOI:
https://doi.org/10.1090/S0002-9939-1973-0320216-6

Keywords:
Free topological groups,
-space,
projective abelian group

Article copyright:
© Copyright 1973
American Mathematical Society