In topology and related branches of mathematics, separated sets are pairs of subsets of a given topological space that are related to each other in a certain way. The notion of when two sets are separated or not is important both to the notion of connected spaces (and their connected components) as well as to the separation axioms for topological spaces.
Separated sets should not be confused with separated spaces (defined below), which are somewhat related but different. Separable spaces are again a completely different topological concept.
Read more about Separated Sets: Definitions, Relation To Separation Axioms and Separated Spaces, Relation To Connected Spaces, Relation To Topologically Distinguishable Points
Famous quotes containing the words separated and/or sets:
“The most puzzling thing about TV is the steady advance of the sponsor across the line that has always separated news from promotion, entertainment from merchandising. The advertiser has assumed the role of originator, and the performer has gradually been eased into the role of peddler.”
—E.B. (Elwyn Brooks)
“The believing mind reaches its perihelion in the so-called Liberals. They believe in each and every quack who sets up his booth in the fairgrounds, including the Communists. The Communists have some talents too, but they always fall short of believing in the Liberals.”
—H.L. (Henry Lewis)