Geodesic
Convex isomorphic ordered sets
Mathematica Bohemica, Tome 118 (1993) no. 1, pp. 29-35

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V. I. Marmazejev introduced in [5] 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 in [1], [2], [4].
V. I. Marmazejev introduced in [5] 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 in [1], [2], [4].
DOI : 10.21136/MB.1993.126018
Classification : 06A06, 06A10, 06B15
Keywords: convex ordered sets; convex isomorphism 
Emanovský, Petr. Convex isomorphic ordered sets. Mathematica Bohemica, Tome 118 (1993) no. 1, pp. 29-35. doi: 10.21136/MB.1993.126018
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