Topological structure of a class of planar self-affine sets

Let T = T(A,D*) be a disk-like Z(2)-tile generated by an expanding 2 x 2 matrix A and a digit set D* subset of Z(2). We study the subset F of T defined by AF = F D, where D subset of D* is a sub-digit set. By studying a periodic extension H = F + Z(2), we classify F into three types according to their topological properties, which generalizes a result of Lau et al. [13]. We also provide some simple criteria for such classification. (C) 2016 Elsevier Inc. All rights reserved.