Connected space

In topology and related branches of mathematics, a connected space is a topological space which cannot be written as the disjoint union of two or more nonempty spaces. Connectedness is one of the principal topological properties that is used to distinguish topological spaces. A stronger notion is that of a path-connected space, which is a space where any two points can be joined by a path.

Examples

• The space of real numbers with the usual topology is connected.
• Every discrete topological space is totally disconnected.
• The Cantor set is totally disconnected.