Free products of topological groups which are -spaces

Author:
Edward T. Ordman

Journal:
Trans. Amer. Math. Soc. **191** (1974), 61-73

MSC:
Primary 22A05

DOI:
https://doi.org/10.1090/S0002-9947-1974-0352320-6

MathSciNet review:
0352320

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Abstract: Let *G* and *H* be topological groups and their free product topologized in the manner due to Graev. The topological space is studied, largely by means of its compact subsets. It is established that if *G* and *H* are -spaces (respectively: countable CW-complexes) then so is . These results extend to countably infinite free products. If *G* and *H* are -spaces, is neither locally compact nor metrizable, provided *G* is nondiscrete and *H* is nontrivial. Incomplete results are obtained about the fundamental group . If and are quotients (continuous open homomorphic images) of *G* and *H*, then is a quotient of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0352320-6

Keywords:
Free product of topological groups,
*k*-space,
-space,
CW-complex,
quotient of topological groups,
nonmetrizable group

Article copyright:
© Copyright 1974
American Mathematical Society