L-模糊化拓扑空间中的Moore-Smith收敛理论

Moore-Smith Convergence in L-Fuzzifying Topological Spaces

中文关键词:  $L$-模糊化拓扑空间  $L$-模糊化滤子  $L$-模糊化网  $L$-模糊化广义收敛空间  拓扑范畴  笛卡尔闭.

英文关键词:$L$-fuzzifying topology  $L$-fuzzifying filter  $L$-fuzzifying net  $L$-fuzzifying generalized convergence space  topological category  cartesian-closed.

中文摘要:

      本文收敛给出了$L$-模糊化网和相应的$L$-模糊化广义收敛空间的定义, 建立了$L$-模糊化拓扑空间中的Moore-Smith收敛理论. 其次, 证明了$L$-模糊化拓扑空间范畴可以作为反射子范畴嵌入到$L$-模糊化广义收敛空间范畴中去, 并且后者是一个笛卡尔闭的拓扑范畴.

英文摘要:

      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 cartesian-closed topological category which embeds the category of $L$-fuzzifying topological spaces as a reflective subcategory.