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N ‐fold sums of Cantor sets
Author(s) -
Hare Kathryn E.,
O'Neil Toby C.
Publication year - 2000
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015850
Subject(s) - mathematics , cantor set , lemma (botany) , cantor function , combinatorics , fold (higher order function) , discrete mathematics , ecology , poaceae , biology , mechanical engineering , engineering
The Newhouse gap lemma is generalized by finding a geometric condition which ensures that N ‐fold sums of compact sets, which might even have thickness zero, are intervals. A new proof is also obtained of a lower bound on the thickness of the sum of two Cantor sets.