Abstract
By a result of Mazurkiewicz and Sierpinski, there exist N, topological types of compact and countable sets.' Since a countable set is 0-dimensional, there arises a natural question: what is the power of topological types of other classes of 0-dimensional sets? In this paper we consider separable metric spaces only. Every 0-dimensional space being topologically contained in the Cantor set2 C, we confine ourselves to subsets of this set. We prove the following three theorems:
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