General topology | Properties of topological spaces

Totally disconnected space

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. (Wikipedia).

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Related pages

Cantor space | Topological space | Metric space | Topology | Stone space | T1 space | Knaster–Kuratowski fan | Rational number | Hausdorff space | Disjoint union (topology) | Connected space | Mathematics | Totally disconnected group | Algebraic number theory | Erdős space | Extremally disconnected space | Baire space (set theory) | Compact space | Equivalence relation | Irrational number | P-adic number | Profinite group | Universal property | Discrete space | Cantor set | Product topology