We introduce the operator given by a hereditary class and a generalized topology μ, and investigate its properties. With the help of , we define -semi-open sets which are generalized open sets on generalized topologies and study the relation between such sets and some generalized open sets (e.g. μ-semi-open sets, μ-β-open sets) on generalized topologies.
 Császár, Á.1997Generalized open setsActa Math. Hungar.7565–87.