可加广义代数格上的 Tietze 扩张定理

数学物理学报

可加广义代数格上的 Tietze 扩张定理

陈学友; 李庆国; 龙飞; 邓自克

山东理工大学数学与信息科学学院淄博 255012

收稿日期:2004-12-10 修回日期:2006-02-13 出版日期:2007-02-25 发布日期:2007-02-25
通讯作者: 陈学友
基金资助:
国家自然科学基金(10471035/A010104)和山东省自然科学基金(2003ZX13)资助

Tietze Extension Theorem on Additive Generalized Algebraic Lattice

Chen Xueyou; Li Qingguo; Long Fei; Deng Zike

College of Mathematics and Information Science, Shandong University of Technology, Zibo 255012

Received:2004-12-10 Revised:2006-02-13 Online:2007-02-25 Published:2007-02-25
Contact: Chen Xueyou

摘要/Abstract

摘要： 可加的广义代数格范畴与 T₀ 拓扑空间范畴相等价, 从这个观点出发, 作者把可加广义代数格作为一个闭集格, 在其上建立 Urysohn 引理和 Tietze 扩张定理. 这是拓扑理论在格上的一种新推广, 有助于格上拓扑理论的研究和广义连续格理论的应用.

关键词: 完备格, 广义代数格, 可加性, 下同态

Abstract: The category of additive generalized algebraic lattices with lower homomorphisms is equivalent to the category of T₀-topological spaces with continuous mappings ([11]). Follow the view, in this paper, using the generalized way below relation, the greatest system of subsets ([11]) and the lower homomorphisms ([12]) as tools, the notion of normal is defined, and Urysohn Lemma, Tietze extension theorem are constructed.

Key words: Complete lattice, Additive property, Generalized algebraic lattice, Lower homomorphism

中图分类号:

06B35

陈学友; 李庆国; 龙飞; 邓自克. 可加广义代数格上的 Tietze 扩张定理[J]. 数学物理学报, 2007, 27(1): 102-108.

Chen Xueyou; Li Qingguo; Long Fei; Deng Zike. Tietze Extension Theorem on Additive Generalized Algebraic Lattice[J]. Acta mathematica scientia,Series A, 2007, 27(1): 102-108.