Decompositions of some weaker forms of continuity

Comparisons of some weak forms of continuity

“…In [3], [12] and [15], the following families were defined: Let f: (X,T)-~ (Y, ga 0 be a mapping, where T and N are topologies on X and Y, respectively. Then f is said to be semi-continuous if f-l(V) ~ SO (X) for each V ~ g~.…”

“…In [15], several families of weak forms of open sets and several weak forms of continuity were defined by Yalvag. Quite recently, Aslim and Ayhan [3] defined several other families of weak forms of open sets and weak [brms of continuity.…”

“…Hence, N C X T% Since T ~ is a topology on X, we have A2 : PO (X) 132.PROOF. VV% learn from[4] that PO (X) A2, and it is clear that A2 C B2, since T C T% Also, we have 132 C PO (X)[3]. Thus A2 PO (X) 132.…”

“…Since o~A(X) c SO (X)[3] and SO (X) c SPO (X), one readily sees that ~A(X) C SPO (X) N ~LC (X).Conversely, let H 6 SPO (X) N ~xLC (X). Dom H 6 SPO (X), we have v c cl 0nt (cl (V))).…”

On decompositions of continuity and some weaker forms of continuity via idealization

“…Quite recently, Aslim and Ayhan [1] have introduced αA-sets, B 1 -sets, B 2 -sets, B 3 -sets and αC-sets to obtain decompositions of some weaker forms of continuity. Janković and Hamlett [9] introduced the notion of I-open sets in ideal topological spaces.…”