Some Properties of Semicontinuous Lattices
XU Ren-fei · Mohu xitong yu shuxue · 2006
In this paper,we discuss some properties of semicontinuous lattices and define a new kind of element--prime element.Through some examples,we reveal that the -prime elements,prime elements and pseudoprime elements are different. The conditions for their equality are given.Moreover,we define a topology on semicontinuous lattices and functions between two semicontinuous lattices.And we prove that the retract of semicontinuous lattice is semicontinuous.