L-序水平一致极限空间

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.

范畴Ω-Cat的函数空间及其性质

Ω-范畴具有范畴论和序理论的双重意义,可为计算机程序语言的语义提供量化的模型,本文研究了范畴Ω-Cat的Ω-值函数空间,得出了Ω-值函数空间函子与Ω-值积函子互为伴随函子,证明了范畴Ω-Cat是Cartesian闭范畴。

Moore-Smith Convergence in L-Fuzzifying Topological Spaces

This paper presents a definition of L-fuzzifying nets and the related L-fuzzifying generalized convergence spaces. The Moore-Smith convergence is established in L-fuzzifying topology. It is shown that the category of L-fuzzifying generalized convergence spaces is a cartesianclosed topological category which embeds the category of L-fuzzifying topological spaces as a reflective subcategory.

T-极限空间范畴的笛卡儿闭性

本文在完备MV-代数的格值环境下,基于T-滤子定义了一种格值收敛空间,即,T-极限空间,并且证明了T-极限空间范畴是拓扑的且具有笛卡儿闭性。同时本文还研究了T-极限空间范畴与其子范畴之间的关系。

双有限liminf domain范畴的笛卡尔闭性

基于模糊偏序集的liminf连续性,引入了双有限liminf domain的概念。这可看作是双有限domain在模糊偏序集框架下的推广。在真值格为frame的情形下,证明了双有限liminf domain范畴是笛卡尔闭的。

Cartesian closedness of categories of completely distributive lattices

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category of completely distributive lattices with nonempty union preserving mappings is cartesian closed.