# totally disconnected space

A topological space $X$ is called totally disconnected if all connected components of $X$ are singletons.

Examples of totally disconnected spaces include:

• Cantor set,

• the set of rational numbers $\mathbb{Q}$ endowed with the subspace topology induced by $\mathbb{Q}\hookrightarrow\mathbb{R}$ and,

• the set of irrational numbers $\mathbb{R}\setminus\mathbb{Q}$ again with the subspace topology.

Title totally disconnected space TotallyDisconnectedSpace 2013-03-22 13:25:31 2013-03-22 13:25:31 Dr_Absentius (537) Dr_Absentius (537) 8 Dr_Absentius (537) Definition msc 54D99 totally disconnected totally disconnected space