Regular interval Cantor sets of S 1 and minimality.

Author’s abstract: It is known that not every Cantor set of S 1 is C 1 -minimal. In this work we prove that every member of a subfamily of what we here call regular interval Cantor set is not C 1 -minimal. We also prove that no member of a class of Cantor sets that includes this subfamily is C 1+∈-minimal, for any ∈> 0