Effective packing dimension of Π⁰₁-classes
Chris J. Conidis · Proceedings of the American Mathematical Society · 2008
We construct a Π 1 0 \Pi ^0_1 -class X X that has classical packing dimension 0 and effective packing dimension 1. This implies that, unlike in the case of effective Hausdorff dimension, there is no natural correspondence principle (as defined by Lutz) for effective packing dimension. We also examine the relationship between upper box dimension and packing dimension for Π 1 0 \Pi ^0_1 -classes.