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Raising dimension under all projections

John Cobb — 1994

Fundamenta Mathematicae

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.

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