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Abstract  

The notion of ⋆-extremally disconnected ideal topological spaces is introduced and studied. Many characterizations of the space are obtained.

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Abstract  

Properties of α-I-open sets, t-I-sets, strong β-I-open sets, S βI-sets and S-I-sets in ideal topological spaces are discussed. Also, we define a new class of sets called semi-I-locally closed sets which contains the class of all I-locally closed sets and is contained in the class of all semilocally closed sets.

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Abstract  

Characterizations and properties of
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-closed sets and
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-open sets are given. A characterization of normal spaces is given in terms of
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-open sets. Also, it is established that an
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-closed subset of an
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-compact space is
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-compact.
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Abstract  

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.

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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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Summary In [6] we introduced and investigated the notions of f I -sets and f I -continuous functions in ideal topological spaces. In this paper, we investigate their further important properties.

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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  

First, we introduce the notion of f I-sets and investigate their properties in ideal topological spaces. Then, we also introduce the notions of R I C-continuous, f I-continuous and contra*-continuous functions and we show that a function f: (X,τ,I) to (Y,ϕ) is R I C -continuous if and only if it is f I-continuous and contra*-continuous.

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