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:

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Every discrete space,

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Cantor set,

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

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the set of irrational numbers $\mathbb{R}\setminus \mathbb{Q}$ again with the subspace topology.
Title  totally disconnected space 

Canonical name  TotallyDisconnectedSpace 
Date of creation  20130322 13:25:31 
Last modified on  20130322 13:25:31 
Owner  Dr_Absentius (537) 
Last modified by  Dr_Absentius (537) 
Numerical id  8 
Author  Dr_Absentius (537) 
Entry type  Definition 
Classification  msc 54D99 
Synonym  totally disconnected 
Defines  totally disconnected space 