The purpose of the present paper is to introduce the concepts of upper and lower *-continuous multifunctions. Several characterizations of upper and lower *-continuous multifunctions are...

In the present paper, some characterizations of ∗-hyperconnected ideal topological spaces are investigated. Moreover, we introduce the notion of S∗-ℐ-hyperconnected ideal topological spaces. Several characterizations of S∗-ℐ-hyperconnected ideal topological spaces are discussed. Furthermore, we introduce and study θ-ℐ-irreducible ideal topological spaces.

Our main purpose is to introduce and investigate the concepts of some forms of spaces via topological ideals. Some characterizations of some forms of spaces via topological ideals are established. Moreover, several properties of ⋆ -monotonically normal ideal topological spaces are considered.

This paper is concerned with the concepts of s(Lambda, sp)-open sets, p(Lambda, sp)-open sets, alpha(Lambda, sp)-open sets, beta(Lambda, sp)-open sets and b(Lambda, sp)-open sets. Some properties of s(Lambda, sp)-open sets, p(Lambda, sp)-open sets, alpha(Lambda, sp)-open sets, beta(Lambda, sp)-open sets and b(Lambda, sp)-open sets are discussed. In particular, the relationships between s(Lambda, sp)-open sets, p(Lambda, sp)-open sets, alpha(Lambda, sp)-open sets, beta(Lambda, sp)-open sets, b(Lambda, sp)-open sets and other related sets are established. Moreover, several characterizations of Lambda(sp)-extremally disconnected spaces are investigated.

This paper is concerned with the concepts of s(Λ, b)-open sets, p(Λ, b)-open sets, α(Λ, b)-open sets, β(Λ, b)-open sets and b(Λ, b) open sets. Some properties of s(Λ, b)-open sets, p(Λ, b)-open sets, α(Λ, b)-open sets, β(Λ, b)-open sets and b(Λ, b)-open sets are investigated. Moreover, several characterizations of weakly (Λ, b)-continuous functions are established.

This paper deals with the concepts of Λp(⋆)-sets and (Λ, p(⋆))-closed sets which are defined by utilizing the notions of pre-I -open sets and pre-I -closed sets. Moreover, we investigate some properties of (Λ, p(⋆))-extremally disconnected ideal topological spaces. Several characterizations of (Λ, p(⋆))-continuous functions are discussed. Especially, we introduce and characterize some low separation axioms of ideal topologies constructed by the concepts of pre-I -open sets and the pre-I -closure operator.