A new simple family of Cantor sets in [formula omitted] all of whose projections are one-dimensional

Abstract

In 1994, J. Cobb described a Cantor set in R3 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 R3 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.