N-fold sums of Cantor sets

Hare, Kathryn and O'Neil, Toby (2000). N-fold sums of Cantor sets. Mathematika, 47(1-2) pp. 243–250.

Abstract

We generalize the Newhouse gap lemma by finding a geometric
condition which ensures that $N$-fold sums of compact sets, which might even have thickness zero, are intervals. We also obtain a new proof of a lower bound on the thickness of the sum of two Cantor sets.

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