Every component of a fractal square is a Peano continuum

摘要

This paper concerns the local connectedness of components of self-similar sets. Let n >= 2 be an integer and let D subset of {0, 1, . .. , n - 1}2. The self-similar set F satisfying F = d is an element of D is locally connected. The same result for three-dimensional analogues of F does not hold. (F + d)/n is called a fractal square.

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