[1]王文静,方进明*.L-序水平一致极限空间[J].四川师范大学学报(自然科学版),2019,(01):30.[doi:10.3969/j.issn.1001-8395.2019.01.004]
 WANG Wenjing,FANG Jinming.L-ordered Level Uniform Limit Spaces[J].Journal of SichuanNormal University,2019,(01):30.[doi:10.3969/j.issn.1001-8395.2019.01.004]
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L-序水平一致极限空间()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2019年01期
页码:
30
栏目:
基础理论
出版日期:
2018-12-15

文章信息/Info

Title:
L-ordered Level Uniform Limit Spaces
文章编号:
1001-8395(2019)01-0030-05
作者:
王文静 方进明*
中国海洋大学 数学科学学院, 山东 青岛 266100
Author(s):
WANG Wenjing FANG Jinming
School of Mathematical Sciences, Ocean University of China, Qingdao 266100, Shandong
关键词:
一致极限 笛卡儿闭性 L-序一致极限空间 L-序水平一致极限空间 双反射子范畴
Keywords:
uniform limit Cartesian-closedness L-ordered uniform limit spaces L-ordered uniform limit spaces dered level uniform limit spaces bireflective subcategory
分类号:
O159; O154
DOI:
10.3969/j.issn.1001-8395.2019.01.004
文献标志码:
A
摘要:
基于满层L-滤子的L-包含序,提出L-序一致极限空间的概念,证明L-序一致极限空间范畴作为拓扑范畴是笛卡儿闭的.同时利用“水平结构”的思想,发现了它的水平空间,即L-序水平一致极限空间.在证明L-序水平一致极限空间范畴与L-序一致极限空间范畴是范畴同构的同时,还建立了L-序水平一致极限空间范畴是文献中L-水平一致极限空间范畴的双反射子范畴这一深入联系.
Abstract:
In this paper, based on the lattice-valued inclusion order relation of stratified L-filters, we propose the concept of L-ordered uniform limit spaces, and show that the category of all L-ordered uniform limit spaces as topological category is Cartesian-closed. Meanwhile, by making use of the idea of “level structure”, we find the level space of L-ordered uniform limit spaces, namely L-ordered level uniform limit spaces. We prove that the category of all L-ordered level uniform limit spaces and the category of all L-ordered uniform limit spaces are isomorphism. In the meantime, we establish the connection that the category of all L-ordered level uniform limit spaces is a bireflective subcategory of the category of all L-level uniform limit spaces.

参考文献/References:

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[3] RICHARDSON G D, KENT D C. Probabilistic convergence spaces[J]. J Austral Math Soc,1996,A61(3):400-420.
[4] JÄGER G. Level spaces for lattice-valued uniform convergence spaces[J]. Quaestiones Math,2008,31(3):255-277.
[5] JÄGER G, BURTON M H. Stratified L-uniform convergence spaces[J]. Quaestiones Math,2005,28(1):11-36.
[6] FANG J M. Stratified L-ordered quasiuniform limit spaces[J]. Fuzzy Sets and Systems,2013,227:51-73.
[7] HOHLE U, SOSTAK A P. Axiomatic foundations of fixed-basis fuzzy topology[C]//Mathematics of Fuzzy Sets:Logic, Topology and Measure Theory. Dordrecht:Kluwer,1999.
[8] CRAIG A, JAGER G. A common framework for lattice-valued uniform spaces and probabilistic uniform limit spaces[J]. Fuzzy Sets and Systems,2009,160:1177-1203.
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备注/Memo

备注/Memo:
收稿日期:2018-06-19 接受日期:2018-08-30
基金项目: 国家自然科学基金(11471297)和山东省自然科学基金(ZR2017MA017)
*通信作者简介: 方进明(1961—),男,教授,主要从事格上拓扑与非经典推理的研究,E-mail:jmfang@ouc.edu.cn
更新日期/Last Update: 2018-12-15