We consider a collection of subsets of a set $X$ defined in terms of a function on $\wp(X)$, called the $\gamma$-open sets, which is not a topology but we show that some of the results established for topologies are valid for this collection. In particular, we define $\delta_\gamma$-open sets in a $\gamma$-space and characterize its properties. Also, we discuss the properties of $\gamma$-rare sets and characterize $\delta_\gamma$-open sets in terms of $\gamma$-rare sets.