Cantor Sets, Cantorvals, and Their Topological Structure
With interesting topological properties, the Cantor set is worth studying for itself. In other areas, topological structures arise that are in fact homeomorphic to the Cantor set. In particular, we see sets that are homeomorphic to the Cantor set which result from the subsums of particular series, as well as linear combinations of algebraic sums of Cantor sets. These also result in what has been termed a Cantorval, which we also investigate.
Agüero, Ángel, "Cantor Sets, Cantorvals, and Their Topological Structure" (2019). ETD Collection for University of Texas, El Paso. AAI13886890.