Linear Extension
A partial order ≤* on a set X is an extension of another partial order ≤ on X provided that for all elements x and y of X, whenever, it is also the case that x ≤* y. A linear extension is an extension that is also a linear (i.e., total) order. Every partial order can be extended to a total order (order-extension principle).
In computer science, algorithms for finding linear extensions of partial orders (represented as the reachability orders of directed acyclic graphs) are called topological sorting.
Read more about this topic: Partially Ordered Set
Famous quotes containing the word extension:
“Slavery is founded on the selfishness of man’s nature—opposition to it on his love of justice. These principles are in eternal antagonism; and when brought into collision so fiercely as slavery extension brings them, shocks and throes and convulsions must ceaselessly follow.”
—Abraham Lincoln (1809–1865)