Monotone insertion of continuous mappings for complete and completely distributive lattices
Xiaobin Zhi · Journal of Xi'an University of Post and Telecommunications · 2005
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.