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- Separable_space abstract "In mathematics a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.Like the other axioms of countability, separability is a "limitation on size", not necessarily in terms of cardinality (though, in the presence of the Hausdorff axiom, this does turn out to be the case; see below) but in a more subtle topological sense. In particular, every continuous function on a separable space whose image is a subset of a Hausdorff space is determined by its values on the countable dense subset.Contrast separability with the related notion of second countability, which is in general stronger but equivalent on the class of metrizable spaces.".
- Separable_space wikiPageID "27855".
- Separable_space wikiPageRevisionID "581250137".
- Separable_space hasPhotoCollection Separable_space.
- Separable_space subject Category:General_topology.
- Separable_space subject Category:Properties_of_topological_spaces.
- Separable_space type Abstraction100002137.
- Separable_space type Possession100032613.
- Separable_space type PropertiesOfTopologicalSpaces.
- Separable_space type Property113244109.
- Separable_space type Relation100031921.
- Separable_space comment "In mathematics a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence.Like the other axioms of countability, separability is a "limitation on size", not necessarily in terms of cardinality (though, in the presence of the Hausdorff axiom, this does turn out to be the case; see below) but in a more subtle topological sense. ".
- Separable_space label "Espace séparable".
- Separable_space label "Espacio separable".
- Separable_space label "Espaço separável".
- Separable_space label "Przestrzeń ośrodkowa".
- Separable_space label "Separabel".
- Separable_space label "Separable space".
- Separable_space label "Separabler Raum".
- Separable_space label "Spazio separabile".
- Separable_space label "Сепарабельное пространство".
- Separable_space label "可分空間".
- Separable_space label "可分空间".
- Separable_space sameAs Separabilní_prostor.
- Separable_space sameAs Separabler_Raum.
- Separable_space sameAs Διαχωρίσιμος_μετρικός_χώρος.
- Separable_space sameAs Espacio_separable.
- Separable_space sameAs Espace_séparable.
- Separable_space sameAs Spazio_separabile.
- Separable_space sameAs 可分空間.
- Separable_space sameAs 분해가능_공간.
- Separable_space sameAs Separabel.
- Separable_space sameAs Przestrzeń_ośrodkowa.
- Separable_space sameAs Espaço_separável.
- Separable_space sameAs m.06y3b.
- Separable_space sameAs Q680081.
- Separable_space sameAs Q680081.
- Separable_space sameAs Separable_space.
- Separable_space wasDerivedFrom Separable_space?oldid=581250137.
- Separable_space isPrimaryTopicOf Separable_space.