A Discussion on a Special Class of Complete Lattices
Xi Wang · Journal of Huaihai Institute of Technology · 2003
The following concepts are introduced: quotient, subalgebra and homomorphism of completely distributive lattices and meet continuous lattices. It is demonstrated that the Cartesian product and the subalgebra of completely distributive lattices are still a completely distributive lattice, and the image of the completely distributive lattices under a surjective homomorphism is also a completely distributive lattice. Finally, an important conclusion on quotients is reached with a similar conclusion arrived at for meet continuous lattices.