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 2^G. Our theorems generalize known results about Z.

Table of Contents

1. Introduction

2. Definitions and connections

3. The proof of the main theorem

           References

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