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Free topological groups

Published online by Cambridge University Press:  09 April 2009

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

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Let X be any Tychonoff space and βX the Stone—Čech compactification of X. Let F(βX) be the Graev free group of βX and let be the subspace topology on the Graev group F(X). Our results demonstrate that this topology is useful and behaves extremely well; the behavior of the free topology still remains enigmatic.

There are various applications, some of which clarify the free topology on F(X), while others improve various results recently published.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 3 , May 1977 , pp. 360 - 365
Copyright
Copyright © Australian Mathematical Society 1977

References

Arhangel'skii, A. V. (1968), ‘Mappings related to topological groups’, Soviet Math. Dokl. 9, 1011–1015.Google Scholar
Borges, C. R. (1966), ‘On stratifiable spaces’, Pacific J. Math. 17, 1–16.CrossRefGoogle Scholar
Graev, M. I. (1962), ‘Free topological groups’, Amer. Math. Soc. Transl. (ser. 1), 8, 305–364.Google Scholar
Hardy, J. P., Morris, S. A. and Thompson, H. B. (to appear), ‘Applications of the Stone-Čech compactification to free topological groups’.Google Scholar
Hyman, D. M. (1968), ‘A category slightly larger than the metric and CW-categories’, Michigan Math. J. 15, 193–214.CrossRefGoogle Scholar
Mack, J., Morris, S. A. and Ordman, E. T. (1973), ‘Free topological groups and the projective dimension of a locally compact abelian group’, Proc. Amer. Math. Soc. 40, 303–308.CrossRefGoogle Scholar
Markov, A. A. (1962), ‘On free topological groups’, Amer. Math. Soc. Transl. (ser. 1) 8, 195–272.Google Scholar
Michael, E. A. (1968), ‘Biquotient maps and cartesian products of quotient maps’, Ann. Inst. Fourier, Grenoble, 18, 2, 287–302.CrossRefGoogle Scholar
Michael, E. A. (1966), ‘N0-spaces’, J. Math. Mech. 15, 983–1002.Google Scholar
Michael, E. A. (1972), ‘A quintuple quotient quest’, Gen. Top. & Appl. 2, 91–138.CrossRefGoogle Scholar
Thomas, B. V. S. (1974), ‘Free topological groups’, Gen. Top. & Appl. 4, 51–72.CrossRefGoogle Scholar