Trees, the Cantor set and the irrational numbers

Abstract

The Cantor set, first described by Smith in about 1874, sits naturally as the limit points of the complete binary tree, showing that the Cantor set is homeomorphic to the topological power 2, where 2 denotes the discrete two-point space. It also illustrates why there is no topological change if we replace 2 here by a discrete n-point space for any n > 1… (More)

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