Topological Closure of Translation Invariant Preorders

• 成果类型: Article
• 署名作者: Ok, Efe A.; Riella, Gil
• 署名单位: New York University; Universidade de Brasilia
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2013.0633
• 发表日期: 2014
• 页码: 737-745
• 关键词: szpilrajn theorem; continuous analog

摘要

Our primary query is to find conditions under which the closure of a preorder on a topological space remains transitive. We study this problem for translation invariant preorders on topological groups. The results are fairly positive; we find that the closure of preorders and normal orders remain as such in this context. The same is true for factor orders as well under quite general conditions. In turn, in the context of topological linear spaces, these results allow us to obtain a simple condition under which the order-duals with respect to a vector order and its closure coincide. Various order-theoretic applications of these results are also provided in the paper.