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. Every bubbling A of a structure of loset I is a structure of preordered set A (not necessarily complete) whose preorder has negatively transitive asymmetric part and every such structure on a given set A can be obtained by bubbling up of certain structure of a loset I, intrinsically encoded in A.
After 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 balloons. Every ballooning A of a structure of loset I is a structure of preordered set A (not necessarily complete) whose preorder has negatively transitive asymmetric part and every such structure on a given set A can be obtained by bubbling up of certain structure of a loset I, intrinsically encoded in A.