On Scattered Convex Geometries

被引：0

作者：

Adaricheva, Kira ^{[1
,2
]}

Pouzet, Maurice ^{[3
,4
]}

机构：

[1] Yeshiva Univ, Dept Math Sci, 245 Lexington Ave, New York, NY 10016 USA

[2] Nazarbayev Univ, Sch Sci & Technol, Dept Math, 53 Kabanbay Batyr Ave, Astana 010000, Kazakhstan

[3] Univ Claude Bernard Lyon1, Univ Lyon, CNRS, Inst Camille Jordan,UMR 5208, 43 Bd 11 Novembre 1918, F-69622 Villeurbanne, France

[4] Univ Calgary, Math & Stat Dept, Calgary, AB T2N 1N4, Canada

来源：

ORDER-A JOURNAL ON THE THEORY OF ORDERED SETS AND ITS APPLICATIONS | 2017年 / 34卷 / 03期

关键词：

Convex geometry; Algebraic lattice; Order-scattered poset; Topologically scattered lattice; Lattices of relatively convex sets; Multi-chains; Lattices of subsemilattices; Lattices of suborders; ORDERED SETS; LATTICES; CHAINS; POSETS;

D O I：

10.1007/s11083-016-9413-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the semilattice of compact elements. In particular, a semilattice Omega(eta), that does not appear among minimal obstructions to order-scattered algebraic modular lattices, plays a prominent role in convex geometries case. The connection to topological scatteredness is established in convex geometries of relatively convex sets.

引用

页码：523 / 550

页数：28

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