电子学报 ›› 2012, Vol. 40 ›› Issue (5): 995-999.DOI: 10.3969/j.issn.0372-2112.2012.05.021

• 学术论文 • 上一篇    下一篇

Heyting系统及其H-空间化表示形式

吴洪博, 石慧君   

  1. 陕西师范大学数学与信息科学学院, 陕西西安 710062
  • 收稿日期:2011-06-08 修回日期:2011-11-15 出版日期:2012-05-25
    • 基金资助:
    • 国家自然科学基金 (No.11171196)

Heyting System and Its Representation by H-Spatilization

WU Hong-bo, SHI Hui-jun   

  1. College of Mathematics and Information Science, Shaanxi Normal Universtity, Xi'an, Shaanxi 710062, China
  • Received:2011-06-08 Revised:2011-11-15 Online:2012-05-25 Published:2012-05-25

摘要: Steven Vickers将拓扑的方法与逻辑理论的结果相结合于专著《Topology via Logic》中建立了拓扑系统,并将这一理论应用于计算机理论的研究.本文借助于拓扑系统的思想和方法,以及Frame结构和Heyting代数的共有性质,以Heyting代数为主体建立了一种新型的代数系统—Heyting系统,建立了Heyting系统之间的恰当的联系方法—H-连续映射;给出了Heyting系统的H-空间化表示形式并对相关性质进行了讨论.本文的工作进一步丰富了Heyting代数的研究方法和拓扑系统的研究内容.

关键词: 拓扑系统, Heyting系统, H-连续映射, H-空间化, 范畴

Abstract: Steven Vickers has proposed the topological system in his work "Topology via Logic" by synthesizing the methods of topology and the theory of logics,which also is applied to study of computers theory.Firstly,with the help of the idea of topological systems and the properties enjoyed by Frame structure and Heyting algebras,the new algebras system-Heyting system is put forward that takes the Heyting algebras as its principal body;Secondly, the suitable method of H-continuous mapping connecting Heyting systems is established;Thirdly,the representation of H-spatialization of a Heyting system is given,and related properties are investigated.The research methods of Heyting algebras and the research contents of topological system are enriched with the work of this paper.

Key words: topological system, heyting system, H-continuous mapping, H-spatialization, category

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