Geodesic
Flow compactifications of nondiscrete monoids, idempotents and Hindman’s theorem
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 319-342.

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We describe the extension of the multiplication on a not-necessarily-discrete topological monoid to its flow compactification. We offer two applications. The first is a nondiscrete version of Hindman’s Theorem, and the second is a characterization of the projective minimal and elementary flows in terms of idempotents of the flow compactification of the monoid.
Classification : 11B75, 37B05, 37B20, 54C60, 54H20
Keywords: flow; Stone-Čech compactification; Hindman’s theorem 
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     author = {Ball, Richard N. and Hagler, James N.},
     title = {Flow compactifications of nondiscrete monoids, idempotents and {Hindman{\textquoteright}s} theorem},
     journal = {Czechoslovak Mathematical Journal},
     pages = {319--342},
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     volume = {53},
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     zbl = {1026.54043},
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Ball, Richard N.; Hagler, James N. Flow compactifications of nondiscrete monoids, idempotents and Hindman’s theorem. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 319-342. http://geodesic.mathdoc.fr/item/CMJ_2003__53_2_a8/