SYNTOPOGENOUS STRUCTURE OIL COMPLETELY DISTRIBUTIVE LATTICE AND ITS CONNECTEDNESS

In this paper, the general theory of syntopogenous structures on compl etely distributive lattices is established. The unified question of co topology, quasi-uniformity and T-structure is investigated. The result s of this paper complete the framework of the topological structure on completely distributive lattices and generalize the corresponding the ory in general and fuzzy topology. Finally, we examine the connectedne ss. The following main results about connectedness are obtained: (1) I f F:(L(1), S-1)-->(L(2), S-2) is an (S-1, S-2)-continuous GOH (functio n), and D is an element of L(1) is S-1-connected element, then F(D) is S-2-connected element. (2) Let C is an element of(L, S) be an S-conne cted element and C less than or equal to D less than or equal to ($) o ver tilde C, then D is an S-connected element. (3) x(1)(L(i), S-i) is connected iff for any i is an element of I, (L(i), S-i) is connected.