L-偏序集映射空间连续性的刻画

Continuity of function spaces of L-posets

设L为完备剩余格,在L-偏序集中引入步函数的概念。基于一般的weight类,得到了L-偏序集映射空间连续性的一个刻画定理。基于以上结果,证明了两个完全代数的L-完备格之间的余连续映射之集是完全代数的。

Let L be a complete residuated lattice. By introducing the concept of step function in L- posets, a characterization theorem for the continuity of function spaces of L-posets with respect to a general choice of a class of weights is proved. Based on this, it is obtained that for two totally algebraic complete L-posets the set of all cocontinuous functions between them is totally algebraic.