Continuity for Multifunctions in Ideal Topological Spaces

Abstract

This article presents the concept of ı ⋆ -continuous multifunctions in ideal topological spaces. Especially, several characterizations of ı ⋆ -continuous multifunctions are investigated. Moreover, the relationships between ı ⋆ -continuity and the other types of continuity for multifunctions are established.

On m-I-Continuous Multifunctions

“…[2]. Quite recently other results are obtained in [8], [9], [4], [31] and other papers. Then we introduce and investigate the notion of an m-I-continuous multifunction F : (X, τ, I) → (Y, σ) which generalizes the results obtained in [36], [37] and [39].…”

“…Then we introduce and investigate the notion of an m-I-continuous multifunction F : (X, τ, I) → (Y, σ) which generalizes the results obtained in [36], [37] and [39]. Furthermore, we introduce the notion of an mi ⋆ -continuous multifunction F : (X, τ, I) → (Y, σ, J) which generalizes the notions of i ⋆ -continuous multifunctions [9] and m-I-continuous multifunctions.…”

“…A multifunction F : (X, τ, I) → (Y, σ, J) is said to be i ⋆ -continuous [9] if for each x ∈ X and each…”

“…By using mIO(X), we introduce and investigate the notions of an m-I-continuous multifunction F : (X, τ, I) → (Y, σ) and mi ⋆ -continuous multifunction F : (X, τ, I) → (Y, σ, J) . The notion of mi ⋆ -continuity is a generalization of m-Icontinuity and i ⋆ -continuity [9].…”