Abstract:

The definition of strong FS-Posets is given. Some properties of strong FS-Posets are discussed, and it is proved that strong FS -Posets not only are continuous, but also are Scott. Based on strong FS-Poset s, the concept of strong FS-Lattices is given. Some properties of strong FS-La tt ices are studied. Strong FS-Lattices are characteristic of the function space. The sufficient and necessary conditions for a continuous lattice to be a s trong FS-Lattice are obtained.

Key words: approximate identity; strong FS-Poset; scott continuous map; continuous lattice