A note on weak structures due to Császár

Weak structures has been introduced by Á. Császár and it has been shown that every generalized topology and every minimal structure is a weak structure. Recently E. Ekici introduced and studied the structure $r(w)$ in a weak structure $w$ on $X$. In general the structure $r(w)$ need not be a topology on $X$. In this paper we have shown that under some conditions $r(w)$ is a topology on $X$. Further, comparision of two weak structures has been studied.