totally disconnected space
A topological space is called totally disconnected if all connected components of 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 endowed with the subspace topology induced by and,
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the set of irrational numbers again with the subspace topology.
Title | totally disconnected space |
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Canonical name | TotallyDisconnectedSpace |
Date of creation | 2013-03-22 13:25:31 |
Last modified on | 2013-03-22 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 |