 A family of sets is called σ-discrete when it is a union of countably many discrete collections, where a family formula_2 of subsets of a space formula_1 is called discrete, when every point of formula_1 has a neighborhood that intersects at most one member of formula_2.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.