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- Extremally_disconnected_space abstract "In mathematics, a topological space is termed extremally disconnected or extremely disconnected if the closure of every open set in it is open. (The term "extremally disconnected" is usual, even though the word "extremally" does not appear in most dictionaries.)An extremally disconnected space that is also compact and Hausdorff is sometimes called a Stonean space. (Note that this is different from a Stone space, which is usually a totally disconnected compact Hausdorff space.) A theorem due to Andrew Gleason says that the projective objects of the category of compact Hausdorff spaces are exactly the extremally disconnected compact Hausdorff spaces. In the duality between Stone spaces and Boolean algebras, the Stonean spaces correspond to the complete Boolean algebras. An extremally disconnected first countable collectionwise Hausdorff space must be discrete. In particular, for metric spaces, the property of being extremally disconnected (the closure of every open set is open) is equivalent to the property of being discrete (every set is open).".
- Extremally_disconnected_space wikiPageID "5783949".
- Extremally_disconnected_space wikiPageLength "2030".
- Extremally_disconnected_space wikiPageOutDegree "19".
- Extremally_disconnected_space wikiPageRevisionID "650902007".
- Extremally_disconnected_space wikiPageWikiLink Abelian_von_Neumann_algebra.
- Extremally_disconnected_space wikiPageWikiLink Andrew_Gleason.
- Extremally_disconnected_space wikiPageWikiLink Andrew_M._Gleason.
- Extremally_disconnected_space wikiPageWikiLink Boolean_algebra_(structure).
- Extremally_disconnected_space wikiPageWikiLink Cambridge_University_Press.
- Extremally_disconnected_space wikiPageWikiLink Category:Properties_of_topological_spaces.
- Extremally_disconnected_space wikiPageWikiLink Cofinite_topology.
- Extremally_disconnected_space wikiPageWikiLink Cofiniteness.
- Extremally_disconnected_space wikiPageWikiLink Collectionwise_Hausdorff_space.
- Extremally_disconnected_space wikiPageWikiLink Compact_space.
- Extremally_disconnected_space wikiPageWikiLink Complete_Boolean_algebra.
- Extremally_disconnected_space wikiPageWikiLink Discrete_space.
- Extremally_disconnected_space wikiPageWikiLink First-countable_space.
- Extremally_disconnected_space wikiPageWikiLink First_countable_space.
- Extremally_disconnected_space wikiPageWikiLink Hausdorff_space.
- Extremally_disconnected_space wikiPageWikiLink Mathematics.
- Extremally_disconnected_space wikiPageWikiLink Metric_space.
- Extremally_disconnected_space wikiPageWikiLink Projective_object.
- Extremally_disconnected_space wikiPageWikiLink Stone_space.
- Extremally_disconnected_space wikiPageWikiLink Stones_representation_theorem_for_Boolean_algebras.
- Extremally_disconnected_space wikiPageWikiLink Stone–Čech_compactification.
- Extremally_disconnected_space wikiPageWikiLink Topological_space.
- Extremally_disconnected_space wikiPageWikiLink Totally_disconnected.
- Extremally_disconnected_space wikiPageWikiLink Totally_disconnected_space.
- Extremally_disconnected_space wikiPageWikiLinkText "Extremally disconnected space".
- Extremally_disconnected_space wikiPageWikiLinkText "Extremally disconnected".
- Extremally_disconnected_space wikiPageWikiLinkText "Stonean".
- Extremally_disconnected_space wikiPageWikiLinkText "extremally disconnected space".
- Extremally_disconnected_space wikiPageWikiLinkText "extremally disconnected".
- Extremally_disconnected_space author "A. V. Arkhangelskii".
- Extremally_disconnected_space hasPhotoCollection Extremally_disconnected_space.
- Extremally_disconnected_space id "E/e037240".
- Extremally_disconnected_space title "Extremally-disconnected space".
- Extremally_disconnected_space wikiPageUsesTemplate Template:Cite_book.
- Extremally_disconnected_space wikiPageUsesTemplate Template:Reflist.
- Extremally_disconnected_space wikiPageUsesTemplate Template:Springer.
- Extremally_disconnected_space wikiPageUsesTemplate Template:Topology-stub.
- Extremally_disconnected_space subject Category:Properties_of_topological_spaces.
- Extremally_disconnected_space type Property.
- Extremally_disconnected_space type Space.
- Extremally_disconnected_space comment "In mathematics, a topological space is termed extremally disconnected or extremely disconnected if the closure of every open set in it is open. (The term "extremally disconnected" is usual, even though the word "extremally" does not appear in most dictionaries.)An extremally disconnected space that is also compact and Hausdorff is sometimes called a Stonean space.".
- Extremally_disconnected_space label "Extremally disconnected space".
- Extremally_disconnected_space sameAs Extremal_unzusammenhängender_Raum.
- Extremally_disconnected_space sameAs Przestrzeń_ekstremalnie_niespójna.
- Extremally_disconnected_space sameAs m.0f4cmt.
- Extremally_disconnected_space sameAs Экстремально_несвязное_пространство.
- Extremally_disconnected_space sameAs Q1385462.
- Extremally_disconnected_space sameAs Q1385462.
- Extremally_disconnected_space sameAs 極端不連通空間.
- Extremally_disconnected_space wasDerivedFrom Extremally_disconnected_space?oldid=650902007.
- Extremally_disconnected_space isPrimaryTopicOf Extremally_disconnected_space.