关于广义序同态的讨论

Discussion on generalized order homomorphism

摘要

讨论广义序同态在各类完全分配格上的性质,指出F₁格上的广义序同态实为经典集合之间的单射所诱导的保序(包含序)映射,为连续格理论和Fuzzy拓扑学的研究提供一些新的思路.

Abstract

The properties of generalized order homomorphisms on all types of completely distributive lattices are discussed. It is pointed out that the generalized order homomorphisms on F₁ lattices are actually order-preserving mappings (containing the order) induced by injection between classical sets, which provides some new ideas for the study of continuous lattices theory and Fuzzy topology.

关键词

广义序同态 / 单射 / 诱导

Key words

generalized order homomorphism / injection / induced

参考文献

[1] 王国俊, 李永明. 拓扑分子格范畴与相关范畴的关系[J]. 科学通报, 1997, 42(4): 347-350.

[2] 张立国. L—Fuzzy拓扑范畴的表现定理[J]. 沈阳理工大学学报, 2008, 27(1): 87-89.

[3] 张立国, 谢琳. Fuzzy拓扑范畴的经典表示[J]. 模糊系统与数学, 2003, 17(1): 41-45.

[4] 张立国. F₁格范畴的表现定理[J]. 辽宁大学学报(自然科学版), 2022, 49(2): 125-128.

[5] 王国俊. L—Fuzzy拓扑空间论[M]. 西安: 陕西师范大学出版社, 1988: 26.

[6] 郑崇友, 樊磊, 崔宏斌. Frame与连续格[M]. 北京: 首都师范大学出版社, 1994: 174.