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. [2] Dontchev , J. , Ganster , M. , Noiri , T. 1999 Unified operation approach of generalized closed sets via topological ideals Math. Japan 49 395 – 401 . [3

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-generalized closed sets and -spaces Mem. Fac. Sci. Kochi Univ. Ser. A, Math. 17 15 – 31 . [10] Dunham , W. 1977

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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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Acta Mathematica Hungarica
Authors: Gulhan Aslim, Aysegul Caksu Guler, and Takashi Noiri

Summary  

A new class of sets called πgs-closed sets is introduced and its properties are studied. Moreover the notions of πgs-T 1/2 spaces and πgs-continuity are introduced.

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Summary New classes of sets called O-closed sets and  Os-closed sets are introduced and studied. Also, we introduce and study O-continuous functions and Os-continuous functions and prove pasting lemma for these functions. Moreover, we introduce classes of topological spaces O-T 1/2 and O-T s.

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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  

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  

The purpose of this paper is to introduce ideal minimal spaces and to investigate the relationships between minimal spaces and ideal minimal spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

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Abstract

We introduce the notion of maximal μ-open and minimal μ-closed sets in a generalized topological space. We also investigate some of their fundamental properties.

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Abstract  

An ideal on a set X is a nonempty collection of subsets of X with heredity property which is also closed under finite unions. The concept of generalized closed sets in bitopological spaces was introduced by Sundaram. In this paper, we introduce and study the concept of generalized closed sets with respect to an ideal in an ideal bitopological space.

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