Properties of α-I-open sets, t-I-sets, strong β-I-open sets, S βI -sets and S-I-sets in ideal topological spaces are discussed. Also, we define a new class of sets called semi-I-locally closed sets which contains the class of all Ilocally closed sets and is contained in the class of all semilocally closed sets.

We characterize codense and completely codense ideals.

Weakly I-continuous functions were introduced and studied by Açikgöz, Noiri and Yüksel [1]. We further extend their study, generalize some of their results and discuss its properties. * Research Supported by UGC-SERO: MRP-685/05.

We consider a collection of subsets of a set X defined in terms of a function on ℘(X), called the γ−open sets, which is not a topology but we show that some of the results established for topologies are valid for this collection. In particular, we define δγ−open sets in a γ−space and characterize its properties. Also, we discuss the properties of γ−rare sets and characterize δ γ −open sets in terms of γ−rare sets.

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.