A new type of closed sets in a topological space, called ωI,γclosed sets, is introduced and studied. Also we studied and characterized the class of spaces having (I, γ)-tightness.

In this paper, we study the stability under direct sums and restrictions of some strong variations of Weyl and Browder type theorems recently introduced in Rashid and Prasad (

In this article, we study a generalizations of some class of functions that are in relation with the notions of continuity when we use the notions of minimal structures also its are characterized. Moreover we show that the notion of m-e * -T 1/2 spaces, given by Ekici [6], is a particular case of the m-(e * )-T 1/2 spaces when its are defined using the notion of m-generalized closed sets.

Given a complex Banach space X, we investigate the stable character of the property (VE) for a bounded linear operator T:X→X, under commuting perturbations that are Riesz, compact, algebraic and hereditarily polaroid. We also analyze sufficient conditions that allow the transfer of property (VE) from the tensorial factors T and S to its tensor product.

In this paper, we introduce the concepts of inversely $\theta$-semi-open and inversely $\theta$-semi-closed functions and obtain their characterizations if it is possible in terms of $\theta$-closure and $\theta$-interior by using sets determined by the fibres of the function. Finally, we obtain its relationships with the strongly $\theta$-continuous.