an:00409959
Zbl 0780.06001
Emanovsk??, Petr
Convex isomorphic ordered sets
EN
Math. Bohem. 118, No. 1, 29-35 (1993).
00013290
1993
j
06A06 06B15
convex ordered sets; convex isomorphism
Summary: \textit{V. I. Marmazeev} introduced [Uporyad. Mnozhestva Reshetki 9, 50-58 (1986; Zbl 0711.06005)] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which lattices are convex isomorphic, in particular for modular, distributive and complemented lattices.
The aim of this paper is to generalize this concept to ordered sets and to characterize convex isomorphic ordered sets in the general case of modular, distributive or complemented ordered sets. These concepts were defined by \textit{I. Chajda} [Arch. Math., Brno 28, No. 1-2, 25-34 (1992)], \textit{I. Chajda} and \textit{J. Rach??nek} [Order 5, 407-423 (1989; Zbl 0674.06003)]\ and \textit{J. Larmerov??} and \textit{J. Rach??nek} [Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 91, Math. 27, 13-23 (1988; Zbl 0693.06003)].
Zbl 0711.06005; Zbl 0693.06003; Zbl 0674.06003