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- Door_space abstract "In mathematics, in the field of topology, a topological space is said to be a door space if every subset is either open or closed (or both). The term comes from the introductory topology mnemonic that "a subset is not like a door: it can be open, closed, both, or neither".Here are some easy facts about door spaces: A Hausdorff door space has at most one accumulation point. In a Hausdorff door space if x is not an accumulation point then {x} is open.To prove the first assertion, let X be a Hausdorff door space, and let x ≠ y be distinct points. Since X is Hausdorff there are open neighborhoods U and V of x and y respectively such that U∩V=∅. Suppose y is an accumulation point. Then U\{x}∪{y} is closed, since if it were open, then we could say that {y}=(U\{x}∪{y})∩V is open, contradicting that y is an accumulation point. So we conclude that as U\{x}∪{y} is closed, X\(U\{x}∪{y}) is open and hence {x}=U∩[X\(U\{x}∪{y})] is open, implying that x is not an accumulation point.".
- Door_space wikiPageID "5075606".
- Door_space wikiPageLength "1366".
- Door_space wikiPageOutDegree "8".
- Door_space wikiPageRevisionID "657299646".
- Door_space wikiPageWikiLink Accumulation_point.
- Door_space wikiPageWikiLink Category:Properties_of_topological_spaces.
- Door_space wikiPageWikiLink Hausdorff_space.
- Door_space wikiPageWikiLink Limit_point.
- Door_space wikiPageWikiLink Mathematics.
- Door_space wikiPageWikiLink Topological_space.
- Door_space wikiPageWikiLink Topology.
- Door_space wikiPageWikiLinkText "door space".
- Door_space hasPhotoCollection Door_space.
- Door_space wikiPageUsesTemplate Template:Cite_book.
- Door_space wikiPageUsesTemplate Template:Reflist.
- Door_space wikiPageUsesTemplate Template:Topology-stub.
- Door_space subject Category:Properties_of_topological_spaces.
- Door_space type Field.
- Door_space type Property.
- Door_space type Space.
- Door_space comment "In mathematics, in the field of topology, a topological space is said to be a door space if every subset is either open or closed (or both). The term comes from the introductory topology mnemonic that "a subset is not like a door: it can be open, closed, both, or neither".Here are some easy facts about door spaces: A Hausdorff door space has at most one accumulation point.".
- Door_space label "Door space".
- Door_space sameAs فضاء_بوابة.
- Door_space sameAs m.0d1m15.
- Door_space sameAs Q5297210.
- Door_space sameAs Q5297210.
- Door_space wasDerivedFrom Door_space?oldid=657299646.
- Door_space isPrimaryTopicOf Door_space.