Countable linear orders with disjoint infinite intervals are mutually orthogonal

被引：4
|
作者：
Delhomme, Christian [1 ]
Zaguia, Imed [2 ]
机构：
[1] Univ Reunion, Fac Sci & Technol, LIM, ERMIT, PTU-2,Rue Joseph Wetzell, F-97490 St Clotilde, Reunion, France
[2] Royal Mil Coll Canada, Dept Math & Comp Sci, POB 17000 Stn Forces, Kingston, ON K7K 7B4, Canada
来源：
DISCRETE MATHEMATICS | 2018年 / 341卷 / 07期
关键词：
Linearly ordered set; Order preserving map; Bichain; Endomorphism; Orthogonal orders; Endomorphism-rigid relational structure;
D O I：
10.1016/j.disc.2018.03.011
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Two linear orderings of a same set are perpendicular if the only self-mappings of this set that preserve them both are the identity and the constant mappings. Two linear orderings are orthogonal if they are isomorphic to two perpendicular linear orderings. We show that two countable linear orderings are orthogonal as soon as each one has two disjoint infinite intervals. From this and previously known results it follows in particular that each countably infinite linear ordering is orthogonal to itself. (C) 2018 Elsevier B.V. All rights reserved.
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页码：1885 / 1899
页数：15
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