Through out this paper , stands for topological space. Let be a topological space and a subset of . A point in is called condensation point of if for each in with in , the set U is un countable [3]. In 1982 the closed set was first introduced by H. Z. Hdeib in [3], and he defined it as: is closed if it contains all its condensation points and the open set is the complement of the closed set. Equivalently. A sub set of a space , is open if and only if for each , there exists such that and is countable. The collection of all open sets of denoted form topology on and it is finer than . Several characterizations of closed sets were provided in [1, 3, 4, 6].
In 2009 in [5] T. Noiri, A. Al-Omari, M. S. M. Noorani introduced and investigated new notions called open, open, open and open sets which are