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The purpose of this paper is to investigate the prope~ies ofpresemlclosed mappings and improve some already established results. Moreover, it is shown that, if the domain space is To, then optimal continuity and homeomorphism coincide (Theorem 4.18).A M S (MOS) subject classification (1980). Primary 54C10.

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.

We give different definitions for g-closed sets, R 0 and R 1 spaces in generalized topological spaces, characterize such spaces and compare with the existing definitions and results.