Abstract
The purpose of the present paper is to introduce and investigate two new classes of continuous multifunctions called upper/lower $e$-$\I$-continuous multifunctions and upper/lower $\delta\beta_I$-continuous multifunctions by using the concepts of $e$-$\I$-open sets and $\delta\beta_I$-open sets. The class of upper/lower $e$-$\I$-continuous multifunctions is contained in that of upper/lower $\delta\beta_I$-continuous multifunctions. Several characterizations and fundamental properties concerning upper/lower $e$-$\I$-continuity and upper/lower $\delta\beta_I$-continuity are obtained.
Highlights
Throughout this paper, (X, τ ) and (Y, σ) mean topological spaces on which no separation axioms are assumed unless explicitly stated
The intersection of all e-I-closed sets containing A is called the eI-closure of A [3] and is denoted by Cle∗(A)
The union of all e-I-open sets of X contained in A is called the e-I-interior [3] of A and is denoted by Int∗e(A)
Summary
Throughout this paper, (X, τ ) and (Y, σ) (or X and Y ) mean topological spaces on which no separation axioms are assumed unless explicitly stated. A subset A of an ideal topological space (X, τ , I) is said to be δβI -open [9] if A ⊂ Cl(Int(δClI ((A))). Upper δβI -continuous) if at a point x ∈ X if for each open set V of Y such that F (x) ⊂ V , there exists U ∈ EIO(X, x)
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