Abstract : This paper is an attempt to study and introduce the notion of $\omega$-dense set in weak structures and the notion of $m$-dense set in minimal structures. We have also investigate the relationships between $\omega$-dense sets, $m$-dense sets, $\sigma(\omega)$ sets, $\pi(\omega)$ sets, $r(\omega)$ sets, $\beta(\omega)$ sets, $m$-{\it semiopen} sets and $m$-{\it preopen} sets. Further we give some representations of the above generalized sets in minimal structures as well as in weak structures.
