Geodesic
Finite union of H-sets and countable compact sets
Colloquium Mathematicum, Tome 65 (1993) no. 1, p. 83.

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In [2], D. E. Grow and M. Insall construct a countable compact set which is not the union of two H-sets. We make precise this result in two directions, proving such a set may be, but need not be, a finite union of H-sets. Descriptive set theory tools like Cantor-Bendixson ranks are used; they are developed in the book of A. S. Kechris and A. Louveau [6]. Two proofs are presented; the first one is elementary while the second one is more general and useful. Using the last one I prove in my thesis, directed by A. Louveau, the existence of a countable compact set which is not a finite union of Dirichlet sets. This result, quoted in [3], is weaker because all Dirichlet sets belong to H. Other new results about the class H and similar classes of thin sets can be found in [4], [1] and [5].
DOI : 10.4064/cm-65-1-83

Sylvain Kahane 1

1 
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Sylvain Kahane. Finite union of H-sets and countable compact sets. Colloquium Mathematicum, Tome 65 (1993) no. 1, p. 83. doi : 10.4064/cm-65-1-83. http://geodesic.mathdoc.fr/articles/10.4064/cm-65-1-83/

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