On semi-g-regular and semi-g-normal spaces ∗ M. Ganster, S. Jafari and G. B. Navalagi Abstract The aim of this paper is to introduce and study two new classes of spaces, called semi-g-regular and semi-g-normal spaces. Semi-g-regularity and semi-g-normality are separation properties obtained by utilizing semi-generalized closed sets. Recall that a subset A of a topological space (X, τ ) is called semi-generalized closed, briefly sg-closed, if the semi-closure of A ⊆ X is a subset of U ⊆ X whenever A is a subset of U and U is semi-open in (X, τ ). 1 Introduction and Preliminaries In 1970, Levine [15] introduced a new and significant notion in General Topology, namely the notion of a generalized closed set. A subset A of a topological space (X, τ ) is called gen- eralized closed, briefly g-closed, if cl(A) ⊆ U whenever A ⊆ U and U is open in (X, τ ) . This notion has been studied extensively in recent years by many topologists. The investigation of generalized closed sets has led to several new and interesting concepts, e.g. new covering properties and new separation axioms weaker than T 1 . Some of these separation axioms have been found to be useful in computer science and digital topology. As an example, the well-known digital line is a T 3/4 space but fails to be a T 1 space (see e.g. [7]). In 1987, Gangulay et al. [11] generalized the usual notions of regularity and normality by replacing ”closed set” with ”g-closed set” in the definitions, thus obtaining the notions of g-regularity and g-normality. * 2000 Math. Subject Classification — Primary: 54A05 ; Secondary: 54D10. Key Words and Phrases: semi-open, semi-generalized closed, semi-g-regular, semi-g-normal. 1