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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 empty set and the one-point sets are connected; in a totally disconnected space these are the ''only'' connected subsets.
An important example of a totally disconnected space is the Cantor set. Another example, playing a key role in algebraic number theory, is the field ''Q''''p'' of ''p''-adic numbers.
==Definition==
A topological space ''X'' is totally disconnected if the connected components in ''X'' are the one-point sets.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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