A decomposition of continuity in ideal topological spaces

Weakly I-continuous functions

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Weakly I-continuous functions were introduced and studied by Açikgöz, Noiri and Yüksel [1]. We further extend their study, generalize some of their results and discuss its properties.

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“…An ideal space (X, τ, I) is said to be an F I -space [1] if cl (A) ⊂ A for every open set A of X. It is defined to prove the following property of weakly I-continuous functions.…”

Some strong and weak form of z-continuity via Cl *

“…Since (X, τ * ) is completely regular, then there exist a continuous functionf such that f (x) = 0 and X \ P ⊆ f −1 ({1}). Then H x = {y : f (y) < 1 3 } is a cozero-set containing the point x. Since every cozero-set is cz * -I set and x ∈ H x ⊆ P .…”

Continuity for Multifunctions in Ideal Topological Spaces

“…Some authors obtained decompositions of continuity. For instance, Açikgöz et al [2] introduced and investigated the notions of weakly-I -continuous and weak ⋆ -I -continuous functions in ideal topological spaces. Donthev [6] introduced the notion of pre-I -open sets and obtained a decomposition of I -continuity.…”