Some fractals associated with Cantor expansions (Q1018299)

We consider a class of fractals generated by the Cantor series expansion. By constructing some homogeneous Moran subset, we prove that these sets have full dimension. This paper studies a class of fractals associated with Cantor series expansions, and proves that these sets have full Hausdorff dimension. A class of fractals which looks even much smaller than the middle third Cantor set surprisingly possesses full dimension. The roots from it have a homogeneous Moran structure \(M(J,\{n_k\},\{c_k\})\) with \(n_k\to \infty\). The author ingeniously defines an infinitely small quantity, delicately designs infinite sequences, accurately constructs the corresponding Moran set, and then successfully proves the conclusion in the paper.