Definition:Continuation of Woset

Definition
Let $\left({S, \preccurlyeq}\right)$ be a woset.

Let $\left({T, \preccurlyeq}\right)$ be a set with an ordering such that:


 * $(1): \quad T$ is an initial segment of $S$
 * $(2): \quad$ The ordering of the elements of $T$ is the same as their ordering in $S$.

Then $S$ is a continuation of $T$.

Also see

 * Extension of Relation: the same concept, but as applied to the general relation