In this paper, we introduce the notions of locally minimal open (resp. locally minimal closed) and s-mean open (resp. s-mean closed) sets at a certain point in a topological space and investigate some properties of such sets. We see that a minimal open (resp. minimal closed) set is locally minimal open (resp. locally minimal closed) at each of its points and the notion of s-mean open (respectively, s-mean closed) sets is stronger than the notion of mean open (respectively, mean closed) sets.
