Abstract
We fully describe the homeomorphism classes of self-contacting symmetric binary fractal trees, and provide the explicit homeomorphisms for the classes. In developing this theory, we introduce new notations, definitions and results regarding symmetric binary fractal trees. The set of tip points at maximal height for a class of trees forms a middle Cantor set. We study various aspects of the holes in self-contacting trees, and the hole locator pairs can be used to describe the homeomorphism classes.
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