On a-star-I-Open Sets and a Decomposition of Continuity

Abstract

In this paper, we introduce a new set namely a$^{\ast }$-I-open set in ideal topological spaces. Besides, we give some properties and characterizations of it. We obtain that it is stronger than pre$^{\ast }$-$I$ -open set with b-open set and weaker than $\delta \beta _{I}$-open set. Finally, we give a decomposition of continuity by using a$^{\ast }$-I-open set as stated the following:" $f:\left( X,\tau ,I\right) \longrightarrow \left( Y,\varphi \right) $ is continuous if and only if it is a$^{\ast }$-$I$-continuous and strongly A$_{I}$-continuous."