Through out this paper, (X ,T) stands for topological space. Let (X ,T) be a topological space and A
a subset of X. A point x in X is called condensation point of A if for each U in T with x in U , the
set U
Ais uncountable [3]. In 1982 the w -closed set was first introduced by H. Z. Hdeib in [3], and
he defined it as: A is w -closed if it contains all its condensation points and the w -open set is the
complement of the w -closed set. Equivalently. A subset W of a space (X,T) , is w -open if and only
if for each xIW , there exists U IT such that xIU and U \W is countable. The collection of all w -
open sets of (X,T) denoted w T form topology on X and it is finer than T . Several characterizations of
w -closed sets were provided in [1, 3, 4, 6]. For a subset A of X, the closure of A and the w -interior of
A will be denoted by cl(A) and int (A) w respectively. The w - interior of the set A defined as the
union of all w - open sets contained in A .
In 2009 in [5] T. Noiri, A. Al-Omari, M. S. M. Noorani introduced and investigated new
notions called a ?w ?open, pre ?w ? open, b ?w ? open and b ?w ? open sets which are weaker
than w -open set. Let us introduce these notions in the following definition