Before revision: Given a loset I, every surjective map p: A --- > I endows the set A with a structure of preordered set by "replacing" the elements of I with their inverse images via p considered as " bubbles " (sets endowed with an equivalence relation), lifting the structure of loset on A, and "agglutinating" this structure with the bubbles.
After revision: Given a linearly ordered set I, every surjective map p: A --- > I endows the set A with a structure of preordered set by "replacing" the elements of I with their inverse images via p considered as " bubbles " (sets endowed with an equivalence relation), lifting the structure of loset on A, and "agglutinating" this structure with the bubbles.