Raising dimension under all projections
Volume 144 / 1994
Fundamenta Mathematicae 144 (1994), 119-128 DOI: 10.4064/fm-144-2-119-128
As a special case of the general question - "What information can be obtained about the dimension of a subset of $ℝ^n$ by looking at its orthogonal projections into hyperplanes?" - we construct a Cantor set in $ℝ^3$ each of whose projections into 2-planes is 1-dimensional. We also consider projections of Cantor sets in $ℝ^n$ whose images contain open sets, expanding on a result of Borsuk.