Remark
18
[0NB]We have added the antisymmetric property to the usual definition of "Directed Set", see [ 16 ] (or other references in [ 42 ] ).
This choice simplify the discussion (in particular it eases the use of concepts already used in the theory of ordered sets, such as maximum and maximal); at the same time, by [2B3], this choice does not hinder the usufulness and power of the theory developed in this Section and in Section [29X].