Semi-bases and Local semi-bases on Semicontinuous Lattices
Yu Chen · Mohu xitong yu shuxue · 2010
In this paper,the concepts of semi-bases and local semi-bases on semicontinuous lattices are introduced.Some properties and equivalent characterizations of semi-bases and local semi-bases are obtained.It is proved that a complete lattice is semicontinuous if and only if it has semi-bases if and only if it has local semi-bases for all points.The concepts of weights and characters on semicontinuous lattices are also introduced.Relations between the weights(resp.,characters) of a semicontinuous lattice and that of the related topological spaces with semi-Scott topology or semi-Lawson topology are discussed.