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:
“But, depend upon it, you will love your native hills the better for being separated from them.”
—Henry David Thoreau (1817–1862)
“Almsgiving tends to perpetuate poverty; aid does away with it once and for all. Almsgiving leaves a man just where he was before. Aid restores him to society as an individual worthy of all respect and not as a man with a grievance. Almsgiving is the generosity of the rich; social aid levels up social inequalities. Charity separates the rich from the poor; aid raises the needy and sets him on the same level with the rich.”
—Eva Perón (1919–1952)