In this paper, we introduce the notion of strongly α-I-open sets in ideal topological spaces and investigate some of their properties. Further we study the continuous functions for the above set and derive the some of their properties. RESUMENEn este trabajo, se introduce la noción del gran conjunto α-I-abierto ideal en espacios topológicos y se investigan algunas de sus propiedades. Además se estudian las funciones continuas para el conjunto y parte de sus propiedades.

The objective of this paper is to obtain the properties of αψcompact spaces by using nets, filterbase, αψ-complete accumulation points and so on. We also investigate some properties of αψ-continuous multifunctions and αψ-compact spaces in the context of multifunction.

In this paper we introduce the notion of upper and lower faintly αψ-continuous multifunctions. The basic properties and characterizaions of such functions are established.

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In this paper we introduce some new separation axioms by utilizing the notions of αψ-p-open sets and αψ-preclosure operator.