What is meant by "Cantor topology"?

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I would like to know what is meant by Cantor topology. Looking at Wikipedia, I was linked to this page about Cantor space

Maybe I am no good reader (english is not my mother tongue) but where in this article is defined what the Cantor topology is?

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1 Answer

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The Cantor topology or Cantor space is the unique perfect, compact, totally disconnected metric space. In other words, all metric space with those properties are homeomorphic to each other. The classic realization of the Cantor space is the middle-thirds Cantor set whose construction you can see here. However, there are other ways to construct topological spaces which are homeomorphic to the middle-thirds Cantor set. For example, if $A$ is any finite set, the countable Cartesian product of $A$ with the product topology is the Cantor space.

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