Decomposition of continuity via b-open set

C- sets and decomposition of continuity in generalized topological spaces

“…Moreover, we prove that some of the results established in [3] are already established results in topological spaces [10]. Some generalizations of these results are also given.…”

On Bitopological γ-open sets

“… open set and a (1, 2) γ-open set are independent as seen in the following examples.  -open set but not (1,2) locally closed and {a, b,c} is (1,2) locally closed but not (1,2)  -open set.  open and F is (1,2) γ-closed .…”

“…Further Tong [4] introduced the concept of t-set and B-set in topological spaces. In 1963 J.C Kelly [5] introduced the concept of bitopological spaces .The purpose of this paper is to introduce the  -open set in bitopological space, study the properties of this set and investigate the relationship between (1,2) γ-open set, (1,2) locally -closed set , (1,2) γ-locally closed set and (1,2) b-open set . In this paper lastly we study comparison of (1,2) γ-open set with (1,2) * -γ-open set .…”

“…(1,2) γopen set and (1, 2) locally closed are independent as seen from the following example.Example 3.8 Let X = {a,b, c, d}, 1  ={{a}, {a,b}, {a, c, d}, ,X}, 2  = {{a},{d}, {a, d}, ,X} (1, 2)  -O(X) = {{a}, {a,b},{a, d},{a, b, d},{a, c, d},  ,X}. (1,2) LC(X) = {{a}, {b},{c},{a, c},{a,b}, {a, b, c},{b, c, d}, {a, c, d},  ,X }.…”

Sets And Functions In Terms Of Local Function

“…Some of the generalized open sets are: preopen sets of Mashhour et al [25], semi-open sets of Levine [24], semi-preopen sets of Andrijevic ´ [5,6] and α-sets of Njåstad [32]. In the field of generalization, the study of b-open set [3,2,6,4,8,9,11,12,17,30,35] For obtaining the generalized open sets, the study of ideal on the topological space is an admissible part. This study was introduced by Kuratowski [23] and Vaidyanathswamy [34].…”