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Free groups, symmetric and reduced products

Published online by Cambridge University Press:  09 April 2009

Carlos R. Borges
Carlos R. Borges
Affiliation:
Department of Mathematics University of California Davis, California 95616, U.S.A.
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Abstract

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We show that, for any Tychonoff space X with base point θ, the infinite symmetric product SP∞ X of X is a subspace of an abelian group A(X) generated by X. (This clarifies the continuity of the multiplication in SP∞ X.) Furthermore, SP∞ X is a retract of A(X). Analogous results hold for reduced product spaces, with respect to non-abelian groups.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 22 A 99; secondary 54 B 15.

Keywords

Infinite symmetric productsreduced product spacesGraev free groupsembeddings and retracts.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 2 , September 1979 , pp. 174 - 178
Copyright
Copyright © Australian Mathematical Society 1979

References

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