Cuts in cyclically ordered sets
Vítězslav Novák · Czechoslovak Mathematical Journal · 1984
An ordered set is a pair (G, is an order on G.An element x e G is called the least element of (G, <) iïï x < y for any y e G ~ {x}; the greatest element is defined dually.If (G, <) is an ordered set and H Я G, then < n Я^ is an order on Я; this order is denoted by <|д or, briefly, also <, and the subset H = (Я, <) is called an ordered subset of the ordered set G = (G, <).An order < on a set G is linear iff* x < }^ or j; < x for any x, y e G, X Ф j; in this case (G, <) is called a linearly ordered set.I.I.Definition.Let (G, z el.A subset A Я G is an initial interval in G iff it has the following property: xeA, yeG, y y e B.