In order to gain a deeper comprehension of rough set theory in arbitrary universes (not only in finite universes), definitions of R-rough set and R-accurate set are presented from the equivalence relations R in arbitrary universes. These definitions are independent of the upper and lower approximations. Based on this, the properties of R-accurate sets are investigated, a determination theorem and a closeness theorem of operations of accurate sets are put forward and proved. Then the properties of the upper and lower approximations are discussed, again, a representation theorem, a comparison theorem and a topological structure theorem of the upper and lower approximations of rough sets are presented and proved. Finally the dependency of a knowledgebase is researched; a representation theorem of positive areas and a determination theorem of dependency of the knowledgebase are given. These results enrich to a certain extent Pawlak's rough set theory. The conception of accurate set in Chinese is updated.