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A coloring property for countable groups

Published online by Cambridge University Press:  22 May 2009

SU GAO ,
STEVE JACKSON  and
BRANDON SEWARD
SU GAO
Affiliation:
Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, TX 76203, U.S.A. e-mail: sgao@unt.edu, jackson@unt.edu, bs_brandon@yahoo.com
STEVE JACKSON
Affiliation:
Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, TX 76203, U.S.A. e-mail: sgao@unt.edu, jackson@unt.edu, bs_brandon@yahoo.com
BRANDON SEWARD
Affiliation:
Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, TX 76203, U.S.A. e-mail: sgao@unt.edu, jackson@unt.edu, bs_brandon@yahoo.com
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Abstract

Motivated by research on hyperfinite equivalence relations we define a coloring property for countable groups. We prove that every countable group has the coloring property. This implies a compactness theorem for closed complete sections of the free part of the shift action of G on 2G. Our theorems generalize known results about .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 3 , November 2009 , pp. 579 - 592
Copyright
Copyright © Cambridge Philosophical Society 2009

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References

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