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Acta Mathematica Hungarica
Authors: E. Hatir, E. Hatir, E. Hatir, T. Noiri, T. Noiri, and T. Noiri

Summary  

We introduce the notions of δ-t-sets, δβ-t-sets, δ-B-continuity and δβ -B-continuity and obtain decompositions of continuity and complete continuity.

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Abstract  

In [1], Açıkgöz et al. introduced and investigated the notions of w-I-continuous and w*-I-continuous functions in ideal topological spaces. In this paper, we investigate their relationships with continuous and θ-continuous functions.

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Abstract  

The aim of this paper is to give a decomposition of a weaker form of continuity, namely gα**-continuity by providing the concepts of K-sets and K-continuity.

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Abstract  

The main purpose of this paper is to introduce *-operfect, τ*-clopen, α-*-closed, strongly α-*-closed and pre-*-closed sets. We compare them and obtain a diagram to show their relationships among these sets and related sets.

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Abstract  

We introduce new classes of sets called Λg-closed sets and Λg-open sets in topological spaces. We also investigate several properties of such sets. It turns out that Λg-closed sets and Λg-open sets are weaker forms of closed sets and open sets, respectively and stronger forms of g-closed sets and g-open sets, respectively.

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Abstract  

We introduce the notions of δ-I- open sets and semi δ-I-continuous functions in ideal topological spaces and investigate some of their properties. Additionally, we obtain decompositions of semi-I-continuous functions and α-I-continuous functions by using δ-I-open sets.

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Abstract  

We study the concepts of α-I-continuity and α-I-openness in ideal topological spaces, and obtain several characterizations and some properties of these functions. Also, we investigate its relationship with other types of functions.

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Abstract  

We introduce and study two new weak separation axioms called ΛΘ-R 0 and ΛΘ-R 1 by using the notions of (Λ,Θ)-open sets and (Λ,Θ)-closure operators.

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Abstract  

In 1986, Tong [13] proved that a function f : (X,τ)→(Y,ϕ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A I-sets and A I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, ϕ) is continuous if and only if it is α-I-continuous and A I-continuous.

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Abstract  

Wilansky [6] introduced the notion of US spaces. It is the purpose of this paper to introduce and investigate the notion of Θs-US spaces.

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