Noun
totally ordered set (plural totally ordered sets)
(set theory) A set having a specified total order.
A set paired with a total order is called a totally ordered set, a linearly ordered set, a simply ordered set, or a chain. Source: Internet
Every finite subset of a non-empty totally ordered set has both upper and lower bounds. Source: Internet
A partial order under which every pair of elements is comparable is called a total order or linear order; a totally ordered set is also called a chain (e. Source: Internet
Examples Examples of directed sets include: * The set of natural numbers N with the ordinary order ≤ is a directed set (and so is every totally ordered set ). Source: Internet
In a totally ordered set, like the real numbers, the concepts are the same. Source: Internet
Indeed, a totally ordered set (with its order topology ) is compact as a topological space if it is complete as a lattice. Source: Internet