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In topology and related branches of mathematics, a totally disconnected space is a topological space that is maximally disconnected, in the sense that it has no non-trivial connected subsets. In every topological space, the singletons (and, when it is considered connected, the empty set) are connected; in a totally disconnected space, these are the only connected proper subsets.
An important example of a totally disconnected space is the Cantor set, which is homeomorphic to the set of p-adic integers. Another example, playing a key role in algebraic number theory, is the field Qp of p-adic numbers.

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