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- Bing_metrization_theorem abstract "In topology, the Bing metrization theorem, named after R. H. Bing, characterizes when a topological space is metrizable. The theorem states that a topological space is metrizable if and only if it is regular and T0 and has a σ-discrete basis. A family of sets is called σ-discrete when it is a union of countably many discrete collections, where a family of subsets of a space is called discrete, when every point of has a neighborhood that intersects at most one member of . Unlike the Urysohn's metrization theorem which provides a sufficient condition for metrization, this theorem provides both a necessary and sufficient condition for a topological space to be metrizable.The theorem was proven by Bing in 1951 and was an independent discovery with the Nagata-Smirnov metrization theorem that was proved independently by both Nagata (1950) and Smirnov (1951). Both theorems are often merged in the Bing-Nagata-Smirnov metrization theorem. It is a common tool to prove other metrization theorems, e.g. the Moore metrization theorem: a collectionwise normal, Moore space is metrizable, is a direct consequence.".
- Bing_metrization_theorem wikiPageID "9712648".
- Bing_metrization_theorem wikiPageRevisionID "549883872".
- Bing_metrization_theorem hasPhotoCollection Bing_metrization_theorem.
- Bing_metrization_theorem subject Category:Theorems_in_topology.
- Bing_metrization_theorem type Abstraction100002137.
- Bing_metrization_theorem type Communication100033020.
- Bing_metrization_theorem type Message106598915.
- Bing_metrization_theorem type Proposition106750804.
- Bing_metrization_theorem type Statement106722453.
- Bing_metrization_theorem type Theorem106752293.
- Bing_metrization_theorem type TheoremsInTopology.
- Bing_metrization_theorem comment "In topology, the Bing metrization theorem, named after R. H. Bing, characterizes when a topological space is metrizable. The theorem states that a topological space is metrizable if and only if it is regular and T0 and has a σ-discrete basis. A family of sets is called σ-discrete when it is a union of countably many discrete collections, where a family of subsets of a space is called discrete, when every point of has a neighborhood that intersects at most one member of .".
- Bing_metrization_theorem label "Bing metrization theorem".
- Bing_metrization_theorem sameAs m.02ppxcr.
- Bing_metrization_theorem sameAs Q17081508.
- Bing_metrization_theorem sameAs Q17081508.
- Bing_metrization_theorem sameAs Bing_metrization_theorem.
- Bing_metrization_theorem wasDerivedFrom Bing_metrization_theorem?oldid=549883872.
- Bing_metrization_theorem isPrimaryTopicOf Bing_metrization_theorem.