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:
“Substances at base divided
In their summits are united;
There the holy essence rolls,
One through separated souls.”
—Ralph Waldo Emerson (1803–1882)
“Wilson adventured for the whole of the human race. Not as a servant, but as a champion. So pure was this motive, so unflecked with anything that his worst enemies could find, except the mildest and most excusable, a personal vanity, practically the minimum to be human, that in a sense his adventure is that of humanity itself. In Wilson, the whole of mankind breaks camp, sets out from home and wrestles with the universe and its gods.”
—William Bolitho (1890–1930)