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:
“The medium is the message. This is merely to say that the personal and social consequences of any medium—that is, of any extension of ourselves—result from the new scale that is introduced into our affairs by each extension of ourselves, or by any new technology.”
—Marshall McLuhan (1911–1980)