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- Uniformizable_space abstract "In mathematics, a topological space X is uniformizable if there exists a uniform structure on X which induces the topology of X. Equivalently, X is uniformizable if and only if it is homeomorphic to a uniform space (equipped with the topology induced by the uniform structure).Any (pseudo)metrizable space is uniformizable since the (pseudo)metric uniformity induces the (pseudo)metric topology. The converse fails: There are uniformizable spaces which are not (pseudo)metrizable. However, it is true that the topology of a uniformizable space can always be induced by a family of pseudometrics; indeed, this is because any uniformity on a set X can be defined by a family of pseudometrics.Showing that a space is uniformizable is much simpler than showing it is metrizable. In fact, uniformizability is equivalent to a common separation axiom:A topological space is uniformizable if and only if it is completely regular.".
- Uniformizable_space wikiPageID "1774701".
- Uniformizable_space wikiPageRevisionID "602970173".
- Uniformizable_space hasPhotoCollection Uniformizable_space.
- Uniformizable_space subject Category:Properties_of_topological_spaces.
- Uniformizable_space subject Category:Uniform_spaces.
- Uniformizable_space type Abstraction100002137.
- Uniformizable_space type Attribute100024264.
- Uniformizable_space type Possession100032613.
- Uniformizable_space type PropertiesOfTopologicalSpaces.
- Uniformizable_space type Property113244109.
- Uniformizable_space type Relation100031921.
- Uniformizable_space type Space100028651.
- Uniformizable_space type UniformSpaces.
- Uniformizable_space comment "In mathematics, a topological space X is uniformizable if there exists a uniform structure on X which induces the topology of X. Equivalently, X is uniformizable if and only if it is homeomorphic to a uniform space (equipped with the topology induced by the uniform structure).Any (pseudo)metrizable space is uniformizable since the (pseudo)metric uniformity induces the (pseudo)metric topology. The converse fails: There are uniformizable spaces which are not (pseudo)metrizable.".
- Uniformizable_space label "Uniformizable space".
- Uniformizable_space sameAs m.05vx3l.
- Uniformizable_space sameAs Q7885139.
- Uniformizable_space sameAs Q7885139.
- Uniformizable_space sameAs Uniformizable_space.
- Uniformizable_space wasDerivedFrom Uniformizable_space?oldid=602970173.
- Uniformizable_space isPrimaryTopicOf Uniformizable_space.