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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 wikiPageRevisionID "595126856".
- Door_space hasPhotoCollection Door_space.
- Door_space subject Category:Properties_of_topological_spaces.
- Door_space subject Category:Topological_spaces.
- Door_space subject Category:Topology.
- Door_space type Abstraction100002137.
- Door_space type Attribute100024264.
- Door_space type MathematicalSpace108001685.
- Door_space type Possession100032613.
- Door_space type PropertiesOfTopologicalSpaces.
- Door_space type Property113244109.
- Door_space type Relation100031921.
- Door_space type Set107999699.
- Door_space type Space100028651.
- Door_space type TopologicalSpaces.
- 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 label "فضاء بوابة".
- Door_space sameAs m.0d1m15.
- Door_space sameAs Q5297210.
- Door_space sameAs Q5297210.
- Door_space sameAs Door_space.
- Door_space wasDerivedFrom Door_space?oldid=595126856.
- Door_space isPrimaryTopicOf Door_space.