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Intersecting Self-Similar Cantor Sets, J. J. P. Veerman
Intersecting Self-Similar Cantor Sets, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We define a self-similar set as the (unique) invariant set of an iterated function system of certain contracting affine functions. A topology on them is obtained (essentially) by inducing the C 1- topology of the function space. We prove that the measure function is upper semi-continuous and give examples of discontinuities. We also show that the dimension is not upper semicontinuous. We exhibit a class of examples of self-similar sets of positive measure containing an open set. If C 1 and C 2 are two self-similar sets C 1 and C 2 such that the sum of their dimensions …