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- Axiom_of_countability abstract "In mathematics, an axiom of countability is a property of certain mathematical objects (usually in a category) that requires the existence of a countable set with certain properties, while without it such sets might not exist.Important countability axioms for topological spaces:sequential space: a set is open if every sequence convergent to a point in the set is eventually in the setfirst-countable space: every point has a countable neighbourhood basis (local base)second-countable space: the topology has a countable baseseparable space: there exists a countable dense subspaceLindelöf space: every open cover has a countable subcoverσ-compact space: there exists a countable cover by compact spacesRelations:Every first countable space is sequential.Every second-countable space is first-countable, separable, and Lindelöf.Every σ-compact space is Lindelöf.A metric space is first-countable.For metric spaces second-countability, separability, and the Lindelöf property are all equivalent.Other examples:sigma-finite measure spaceslattices of countable type".
- Axiom_of_countability wikiPageID "346611".
- Axiom_of_countability wikiPageRevisionID "540860834".
- Axiom_of_countability hasPhotoCollection Axiom_of_countability.
- Axiom_of_countability subject Category:General_topology.
- Axiom_of_countability subject Category:Mathematical_axioms.
- Axiom_of_countability type Abstraction100002137.
- Axiom_of_countability type AuditoryCommunication107109019.
- Axiom_of_countability type Communication100033020.
- Axiom_of_countability type MathematicalAxioms.
- Axiom_of_countability type Maxim107152948.
- Axiom_of_countability type Saying107151380.
- Axiom_of_countability type Speech107109196.
- Axiom_of_countability comment "In mathematics, an axiom of countability is a property of certain mathematical objects (usually in a category) that requires the existence of a countable set with certain properties, while without it such sets might not exist.Important countability axioms for topological spaces:sequential space: a set is open if every sequence convergent to a point in the set is eventually in the setfirst-countable space: every point has a countable neighbourhood basis (local base)second-countable space: the topology has a countable baseseparable space: there exists a countable dense subspaceLindelöf space: every open cover has a countable subcoverσ-compact space: there exists a countable cover by compact spacesRelations:Every first countable space is sequential.Every second-countable space is first-countable, separable, and Lindelöf.Every σ-compact space is Lindelöf.A metric space is first-countable.For metric spaces second-countability, separability, and the Lindelöf property are all equivalent.Other examples:sigma-finite measure spaceslattices of countable type".
- Axiom_of_countability label "Abzählbarkeitsaxiom".
- Axiom_of_countability label "Aftelbaarheidsaxioma".
- Axiom_of_countability label "Aksjomaty przeliczalności".
- Axiom_of_countability label "Assioma di numerabilità".
- Axiom_of_countability label "Axiom of countability".
- Axiom_of_countability sameAs Abzählbarkeitsaxiom.
- Axiom_of_countability sameAs Assioma_di_numerabilità.
- Axiom_of_countability sameAs Aftelbaarheidsaxioma.
- Axiom_of_countability sameAs Aksjomaty_przeliczalności.
- Axiom_of_countability sameAs m.010xcwzn.
- Axiom_of_countability sameAs Q336779.
- Axiom_of_countability sameAs Q336779.
- Axiom_of_countability sameAs Axiom_of_countability.
- Axiom_of_countability wasDerivedFrom Axiom_of_countability?oldid=540860834.
- Axiom_of_countability isPrimaryTopicOf Axiom_of_countability.