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It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated if there exists an intermediate sequence, containing a point from each hyperbolic geodesic which connects any two points from the original sequence, and whose separated subsequences are uniformly separated. This result is applied to improve recent results on the zero distribution of solutions of linear differential equations in the unit disc.

Uniform separation, hyperbolic geodesics and zero distribution of solutions of linear differential equations