The Cantor Set -- Ilya Vinogradov
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I will introduce the Cantor set using the elementary construction by removing middle thirds of intervals from [0,1). Then, I will show that it is a compact, perfect, totally disconnected topological space. Next, I will explain its significance to dynamical systems and give other ways of coming up with it. Finally, I will state that any topological space with the three above properties is homeomorphic to the Cantor set.