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- Hyperconnected_space abstract "In mathematics, a hyperconnected space is a topological space X that cannot be written as the union of two non-empty closed sets (whether disjoint or non-disjoint). The name irreducible space is preferred in algebraic geometry.For a topological space X the following conditions are equivalent: No two nonempty open sets are disjoint. X cannot be written as the union of two proper closed sets. Every nonempty open set is dense in X. The interior of every proper closed set is empty.A space which satisfies any one of these conditions is called hyperconnected or irreducible.An irreducible set is a subset of a topological space for which the subspace topology is irreducible. Some authors do not consider the empty set to be irreducible (even though it vacuously satisfies the above conditions).".
- Hyperconnected_space wikiPageID "7556651".
- Hyperconnected_space wikiPageLength "4167".
- Hyperconnected_space wikiPageOutDegree "37".
- Hyperconnected_space wikiPageRevisionID "667932697".
- Hyperconnected_space wikiPageWikiLink Algebraic_geometry.
- Hyperconnected_space wikiPageWikiLink Algebraic_variety.
- Hyperconnected_space wikiPageWikiLink Category:Properties_of_topological_spaces.
- Hyperconnected_space wikiPageWikiLink Closed_set.
- Hyperconnected_space wikiPageWikiLink Closure_(topology).
- Hyperconnected_space wikiPageWikiLink Cofinite_topology.
- Hyperconnected_space wikiPageWikiLink Cofiniteness.
- Hyperconnected_space wikiPageWikiLink Connected_component_(topology).
- Hyperconnected_space wikiPageWikiLink Connected_space.
- Hyperconnected_space wikiPageWikiLink Continuous_function.
- Hyperconnected_space wikiPageWikiLink Continuous_function_(topology).
- Hyperconnected_space wikiPageWikiLink Counterexamples_in_Topology.
- Hyperconnected_space wikiPageWikiLink Dense_(topology).
- Hyperconnected_space wikiPageWikiLink Dense_set.
- Hyperconnected_space wikiPageWikiLink Disjoint_sets.
- Hyperconnected_space wikiPageWikiLink Dover_Publications.
- Hyperconnected_space wikiPageWikiLink Empty_set.
- Hyperconnected_space wikiPageWikiLink Hausdorff_space.
- Hyperconnected_space wikiPageWikiLink Interior_(topology).
- Hyperconnected_space wikiPageWikiLink Irreducible_component.
- Hyperconnected_space wikiPageWikiLink Locally_connected.
- Hyperconnected_space wikiPageWikiLink Locally_connected_space.
- Hyperconnected_space wikiPageWikiLink Locally_path-connected.
- Hyperconnected_space wikiPageWikiLink Mathematics.
- Hyperconnected_space wikiPageWikiLink Noetherian_topological_space.
- Hyperconnected_space wikiPageWikiLink Open_set.
- Hyperconnected_space wikiPageWikiLink Partition_of_a_set.
- Hyperconnected_space wikiPageWikiLink Path-connected.
- Hyperconnected_space wikiPageWikiLink Pseudocompact_space.
- Hyperconnected_space wikiPageWikiLink Singleton_(mathematics).
- Hyperconnected_space wikiPageWikiLink Singleton_set.
- Hyperconnected_space wikiPageWikiLink Sober_space.
- Hyperconnected_space wikiPageWikiLink Springer-Verlag.
- Hyperconnected_space wikiPageWikiLink Springer_Science+Business_Media.
- Hyperconnected_space wikiPageWikiLink Subspace_topology.
- Hyperconnected_space wikiPageWikiLink Topological_space.
- Hyperconnected_space wikiPageWikiLink Ultraconnected_space.
- Hyperconnected_space wikiPageWikiLink Vacuous_truth.
- Hyperconnected_space wikiPageWikiLink Zariski_topology.
- Hyperconnected_space wikiPageWikiLinkText "Hyper-connected".
- Hyperconnected_space wikiPageWikiLinkText "Hyperconnected space".
- Hyperconnected_space wikiPageWikiLinkText "hyperconnected space".
- Hyperconnected_space wikiPageWikiLinkText "hyperconnected".
- Hyperconnected_space wikiPageWikiLinkText "irreducible".
- Hyperconnected_space hasPhotoCollection Hyperconnected_space.
- Hyperconnected_space id "5813".
- Hyperconnected_space title "Hyperconnected space".
- Hyperconnected_space wikiPageUsesTemplate Template:Citation.
- Hyperconnected_space wikiPageUsesTemplate Template:For.
- Hyperconnected_space wikiPageUsesTemplate Template:No_footnotes.
- Hyperconnected_space wikiPageUsesTemplate Template:Planetmath_reference.
- Hyperconnected_space subject Category:Properties_of_topological_spaces.
- Hyperconnected_space hypernym X.
- Hyperconnected_space type Work.
- Hyperconnected_space type Property.
- Hyperconnected_space type Space.
- Hyperconnected_space comment "In mathematics, a hyperconnected space is a topological space X that cannot be written as the union of two non-empty closed sets (whether disjoint or non-disjoint). The name irreducible space is preferred in algebraic geometry.For a topological space X the following conditions are equivalent: No two nonempty open sets are disjoint. X cannot be written as the union of two proper closed sets. Every nonempty open set is dense in X.".
- Hyperconnected_space label "Hyperconnected space".
- Hyperconnected_space sameAs Irreduzibler_topologischer_Raum.
- Hyperconnected_space sameAs Espacio_hiperconexo.
- Hyperconnected_space sameAs Espace_topologique_irréductible.
- Hyperconnected_space sameAs 既約位相空間.
- Hyperconnected_space sameAs 기약_공간.
- Hyperconnected_space sameAs Przestrzeń_nieprzywiedlna.
- Hyperconnected_space sameAs Espaço_hiperconectado.
- Hyperconnected_space sameAs m.02657y0.
- Hyperconnected_space sameAs Гіперзв’язний_простір.
- Hyperconnected_space sameAs Q1673182.
- Hyperconnected_space sameAs Q1673182.
- Hyperconnected_space wasDerivedFrom Hyperconnected_space?oldid=667932697.
- Hyperconnected_space isPrimaryTopicOf Hyperconnected_space.