Minkowski's chain characterizes badly approximable forms by a smallest-error term bounded away from zero, singular forms by that term tending to zero, and badly approximable forms by existence of a basis of approximating integer vectors.
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The Minkowski chain and Diophantine approximation
Minkowski's chain characterizes badly approximable forms by a smallest-error term bounded away from zero, singular forms by that term tending to zero, and badly approximable forms by existence of a basis of approximating integer vectors.