Abstract:

For an abitrary set X, appropriate order relations on    WCL(X) (the set of all weak closure operators), WIN(X) (the set of all weak interior operators), WOU(X) (the set of all weak exterior operators), WB(X) (the set of all weak boundary operators), WD(X) (the set of all weak derived operators), WD*(X) (the set of all weak difference derived operators), WR(X) (the set of all weak remote neighborhood system operators) and WN(X) (the set of all weak neighborhood system operators) can be defined respectively, which make WCL(X), WIN(X), WOU(X), WB(X), WD(X), WD*(X), WR(X) and WN(X) to be complete lattices that are ismorphic to (CS(X),CS(X) is the set of all closure systems on X.

Key words: closure system; weak interior operator; weak exterior  operator; weak  boundary operator; weak difference derived operator; weak remote neighborhood s ystem operator