Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information systems. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations, or partitions. This paper studies covering-based generalized rough sets. In this setting, a covering can also generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a covering under which these properties hold for the covering-based lower and upper approximation operations.