Computer Engineering and Applications ›› 2011, Vol. 47 ›› Issue (2): 38-40.DOI: 10.3778/j.issn.1002-8331.2011.02.012

• 研究、探讨 • Previous Articles     Next Articles

Some kinds of many-valued orders and their application in topology

LI Lingqiang,JIN Qiu   

  1. Department of Mathematics Science,Liaocheng University,Liaocheng,Shandong 252059,China
  • Received:2009-09-14 Revised:2009-10-28 Online:2011-01-11 Published:2011-01-11
  • Contact: LI Lingqiang

几种多值序及其在拓扑中的应用

李令强,金 秋   

  1. 聊城大学 数学科学学院,山东 聊城 252059
  • 通讯作者: 李令强

Abstract: In this paper,some kinds of many-valued orders are studied and their application in topology is investigated.In precisely,for an arbitrary complete residuated lattice (Ω,*,1),the Ω-filter Monad (FΩ,η,μ) is constructed from the viewpoint of many-valued order and then the negighborhood system of strong Ω-topology is presented.This shows the closed interrelationship between topologcial sturcutre,ordered structure and category.

Key words: many-valued orders, Monad diagonal operator, many-valued topology, many-valued filter

摘要: 讨论了几种常见的多值序结构及其在拓扑中的应用。具体来说,对任意完备剩余格(Ω,*,1),从多值序的角度出发构造了Ω-滤子 Monad (FΩ,η,μ),并据此给出了强Ω-拓扑的邻域结构,并展示了拓扑、序和范畴三种不同的结构之间的密切联系。

关键词: 多值序, Monad对角运算, 多值拓扑, 多值滤子

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