L集合范畴的格值函数空间及其性质

The Lattice-valued Functional Spaces and the Property in the Category of L-Sets

引入了L集合范畴中的一些基本概念,研究了L集合范畴的两种函数空间,即格值函数空间与伪格值函数空间,进一步指出了格值函数空间函子与格值积函子互为伴随,伪格值函数空间函子与格值并函子也互为伴随,并讨论了关于格值函数空间与伪格值函数空间的部分性质.

In this paper we introduced some conceptions in the category of L-Sets,and researched the two kinds of functional spaces in this category,which are the lattice-valued functional space and the pseudo lattice-valued functional space. Finally,we found the lattice-valued functional space functor is a right adjoin for the lattice-valued product functor,in other words,the category of L-Sets is Cartesian closed,and the pseudo lattice-valued functional space functor is also a right adjoint for the lattice-valued join functor.