完备的完全分配格上连续映射的单调插入

Monotone insertion of continuous mappings for complete and completely distributive lattices

探讨对于完备的完全分配格Diendonne’-Hahn-Tong定理的单调插入性质,我们把所有的格值(下)半连续映射的族看作一个拓扑,然后对于一个合适的格得到以下结果:诱导空间是单调正规的当且仅当它的下方空间是单调正规的,也即证明了:拓扑空间是单调正规的当且仅当对于具有可数严格并生成集的完备的完全分配格具有单调插入性质。

In this paper, We have studied the property of monotone insertion of Hahn- Dieudone-Tong Theorem for complete and completely distributive lattices. We consider the family of all lattice - valued (lower) semicontinuous mappings as a topology and get the conclusion: An induced space is monotone normal if and only if the underlying space is normal. Viz a topology space is monotone normal if and only if it has the property of monotone insertion for the complete and completely distributive lattice which has a countable strictly join-generating set.