Z-Semicontinuous Lattice
Xiaoquan Xu · Mohu xitong yu shuxue · 2012
As a common generalization of continuous lattice and semicontinuous lattices,the concepts of generalized ideal sub-systems,Z-semicontinuous and strongly Z-continuous lattices are introduced,and some basic properties and the structures of function spaces on Z-semicontinuous lattices and strongly Z-continuous lattices are investigated,and an embedding theorem for strongly Z-continuous lattices into a cube is given.It is proved that category SCLZ on Z-semicontinuous lattices is Cartesian closedness when it satisfies certain conditions.