Directed set

A directed set called in mathematics a nonempty set equipped with a relation over ( called direction) which satisfies the following axioms:

To highlight the direction ( on a lot of may well be explained several directions ), also called the ordered pair directed set. Speech for "x before y " or " y to x ". These are understood.

Equivalent could be a directed set as a non-empty quasi-ordering in which every finite non- empty subset has an upper bound, define. In particular, each direction is therefore a quasi-ordering.

Examples

• Any amount and

• Order theory
• Set topology