Raising dimension under all projections

As a special case of the general question - "What information can be obtained about the dimension of a subset of ${\displaystyle {ℝ}^n}$ by looking at its orthogonal projections into hyperplanes?" - we construct a Cantor set in ${\displaystyle {ℝ}^3}$ each of whose projections into 2-planes is 1-dimensional. We also consider projections of Cantor sets in ${\displaystyle {ℝ}^n}$ whose images contain open sets, expanding on a result of Borsuk.