• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Order >The Geometry of Relations
【24h】

The Geometry of Relations

机译：关系的几何

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The classical way to study a finite poset (X,≤) using topology is by means of the simplicial complex △_X of its nonempty chains. There is also an alternative approach, regarding X as a finite topological space. In this article we introduce new constructions for studying X topologically: inspired by a classical paper of Dowker (Ann Math 56:84-95,1952), we define the simplicial complexes K_X and L_X associated to the relation ≤. In many cases these polyhedra have the same homotopy type as the order complex △_X. We give a complete characterization of the simplicial complexes that are the K or L-complexes of some finite poset and prove that K_X and K_X are topologically equivalent to the smaller complexes K'_X, L'_X induced by the relation <. More precisely, we prove that K_X (resp. L_X) simplicially collapses to K'_X (resp. L'_X). The paper concludes with a result that relates the K-complexes of two posets X, Y with closed relations R is contained in X × Y.
机译：使用拓扑研究有限姿态（X，≤）的经典方法是借助其非空链的简单复数△_X。还有另一种方法，将X视为有限的拓扑空间。在本文中，我们介绍了用于拓扑学研究X的新结构：受Dowker的经典论文启发（Ann Math 56：84-95,1952），我们定义了与关系≤相关的单纯形复数K_X和L_X。在许多情况下，这些多面体与同级复数△_X具有相同的同伦类型。我们给出了一些有限姿态的K或L复合物的简单复合物的完整表征，并证明K_X和K_X在拓扑上等效于由关系<引起的较小的复合物K'_X，L'_X。更确切地说，我们证明K_X（分别为L_X）简单地崩溃为K'_X（分别为L'_X）。本文的结论是，两个坐式X，Y的K络合物与封闭关系R包含在X×Y中。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号