# Zero-dimensional perfect compact space is Cantor set

## Theorem

A topological space is homeomorphic to the Cantor set if and only if it is zero-dimensional, perfect, and it is a compactum.

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A topological space is homeomorphic to the Cantor set if and only if it is zero-dimensional, perfect, and it is a compactum.

- This page was last edited on 23 September 2016, at 14:10.