A new simple family of Cantor sets in ${\mathbb{R}}^3$ all of whose projections are one-dimensional

Abstract

In 1994, J.Cobb described a Cantor set in ${\mathbb{R}}^3$ each of whose projections into 2-planes is one-dimensional. A series of works by other authors developing this field followed. We present another very simple series of Cantor sets in ${\mathbb{R}}^3$ all of whose projections are connected and one-dimensional. These are self-similar Cantor sets which go back to the work of Louis Antoine, and we celebrate their centenary birthday in 2020-2021.

References in corpus (2)

• Cantor sets with high-dimensional projections
• All projections of a typical Cantor set are Cantor sets