A Kolmogorov complexity characterization of constructive Hausdorff dimension
Information Processing Letters
The dimensions of individual strings and sequences
Information and Computation
Correspondence Principles for Effective Dimensions
Theory of Computing Systems
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We prove that the set of all points of effective Hausdorff dimension 1 in R^n(n=2) is connected, and simultaneously that the complement of this set is not path-connected when n=2.