Disconnected space

Totally disconnected space

In topology and related branches of mathematics, a totally disconnected space is a topological space which 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 Qp of p-adic numbers.


A topological space X is totally disconnected if the connected components in X are the one-point sets.


The following are examples of totally disconnected spaces:



See also

Search another word or see Disconnected spaceon Dictionary | Thesaurus |Spanish
Copyright © 2015, LLC. All rights reserved.
  • Please Login or Sign Up to use the Recent Searches feature