Topology Proceedings 28 No. 2 (2004), pp. 361-399

The Graham-Rothschild Theorem and the algebra of \betaW

Timothy J. Carlson, Neil Hindman and Dona Strauss

In a previous paper we established an infinitary extension of the Graham-Rothschild Theorem by producing an infinite decreasing chain of idempotents in the Stone-Cech compactification of the set of variable words over a nonempty alphabet. In this paper we investigate further the algebraic structure of that compactification and determine which finite chains of idempotents are extendable to an infinite chain as above.

Keywords: Graham-Rothschild Theorem, variable words, free semigroup, Stone-Cech compactification

Mathematics Subject Classification: 54D35 (54H15 05D10)

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Topology Proceedings, Volume 28, No. 2 (2004)
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