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Diophantine approximation and badly approximable sets
2006
Advances in Mathematics
Let (X, d) be a metric space and ( , d) a compact subspace of X which supports a nonatomic finite measure m. We consider 'natural' classes of badly approximable subsets of . Loosely speaking, these consist of points in which 'stay clear' of some given set of points in X. The classical set Bad of 'badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i, j ) of simultaneously badly approximable numbers. Under various natural
doi:10.1016/j.aim.2005.04.005
fatcat:sqxcszbpprfvdinm77mbxukr5m