A new collection which contains the topology via ideals

Abstract

In 1999, Dontchev studied the concept of pre-$I$-open sets (Dontchev, 1999). In 2002, Hatir and Noiri studied the concept of semi-$I$-open sets (Hatir and Noiri, 2002). In 2013, Ekici studied the concept of $C_I^{\ast }$-sets (Ekici, 2013). In this paper, the concept of $\zeta$-$I$-open sets is introduced. The concept of $\zeta$-$I$-open sets is related to topology, pre-$I$-open sets, semi-$I$-open sets and $C_I^{\ast }$-sets. Main properties of $\zeta$-$I$-open sets are presented.