Irreducible space: Difference between revisions
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{{topospace property}} | {{topospace property}} | ||
==Definition== | == Definition == | ||
===Symbol-free definition=== | === Symbol-free definition === | ||
A [[topological space]] is said to be '''irreducible''' if it cannot be expressed as a union of two proper closed subsets. | A [[Topological space|topological space]] is said to be '''irreducible''' if it is nonempty and cannot be expressed as a union of two proper closed subsets. | ||
==Relation with other properties== | == Relation with other properties == | ||
===Weaker properties=== | === Weaker properties === | ||
* [[Noetherian space]] | * [[Noetherian space]] | ||
* [[Connected space]] | * [[Connected space]] | ||
Revision as of 01:41, 10 January 2008
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
Definition
Symbol-free definition
A topological space is said to be irreducible if it is nonempty and cannot be expressed as a union of two proper closed subsets.