Nakaoka and Oda ([9] and [10]) introduced the notion of maximal open sets and minimal closed sets. In this paper, we introduce new classes of sets called maximal βθ-open sets, minimal βθ-closed sets, βθ-semi maximal open sets and βθ-semi minimal closed sets and investigate some of their fundamental properties.
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In this paper, we introduce the notion of contra (mX, mY)-semicontinuous functions between m-spaces. We obtain many characterizations of these functions and deal with decompositions of the functions and other related functions.
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The notion of weakly δs-continuous functions is introduced by Ekici in [6]. In this paper, we further investigate some more properties of weakly δs-continuous functions. This type of continuity is a generalization of super continuity [16].
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In this paper we introduce the concepts of Ʌɯ-sets and Vɯ-sets in a weak structure space due to Császár. It is shown that many results in previous papers can be considered as special cases of our results.
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We introduce a new notion called slightly (μ,λ)-continuous functions on generalized topological spaces. Furthermore, basic properties and preservation theorems of slightly (μ,λ)-continuous functions are investigated and relationships between slightly (μ,λ)-continuous functions and graphs are investigated.
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In this paper, πg-closed sets and πg-open sets are used to define and investigate a new class of functions called, totally πg-continuous functions. Relationships between this new class and other classes of related functions are established.
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We introduce the notion of mIT-structures determined by operators mint and mCl on an m-space (X, mX). By using mIT-structures, we introduce and investigate a function f : (X, mIT) → (Y, mY) called MIT-continuous. As special cases of M/T -continuity, we obtain M-semicontinuity [21] and M-precontinuity [23].
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We obtain the further properties of quasi Mconti¬nuous functions which were introduced and investigated in order to establish the unified theory for several variations of quasi-conti¬nuity between bitopological spaces.
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In this paper, by using mg*-closed sets [23], we define and investigate the notion of mg*-continuity which is a generalization of ω-continuity [32] or g-continuity [35].
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We introduce a new class of sets called u-m-open sets which are defined on a family of sets satisfying m-structures with the property of being closed under arbitrary union. The sets enable us to obtain some unified properties of certain types of generalizations of Lindelof spaces.
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A new weak form of both slightly continuous and ω-continuous, called slightly ω-continuous, is introduced and studied. Furthermore, basic properties and preservation theorems of slightly ω-continuous functions are investigated. Relationships between slightly ω-continuous functions and set ω-connected functions are investigated.
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By using m-open multifunctions from a topological space into an m-space, we establish the unified theory for several weak forms of open multifunctions in the sense of Kuratowski between bitopological spaces.
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In this paper, we introduce and study two new classes of functions called weakly b-Q-open functions and weakly b-Q-closed functions by using the notions of b-Q-open sets and b-Q-closure operator. The connections between these functions and other related functions are investigated.
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As a generalization of weakly continuous functions, we introduce the notion of (i, j)-weakly m-continuous functions in bitopological spaces and obtain unified characterizations and properties of certain forms of weakly continuous functions in bitopological spaces.
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By using the notion of m-spaces, we establish the unified theory for several variations of separation axioms quasi TO, quasi T1 and quasi T2 in bitopological spaces.
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In this paper we obtain new characterizations of upper and lower θ-quasicontinuous muitifunctions and investigate several properties of such multifunctions.
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The aim of this paper is to introduce and study gamma alfa-continuous functions as a generalization of preirresoluteness, alfa-precontinuity, alfa-irresoluteness, gamma-irresoluteness, irresoluteness and semi alfa-irresoluteness. Furthermore, basic characterizations, preservation theorems and several properties concerning gamma alfa-continuous functions are investigated. The relationships between gamma alfa-continuous functions and the other types of continuity are also discussed.
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It is shown that a subset A of a topological space (X, r) is (^semi-open (resp. preopen) in (X,r) if and only if it is semi-open (resp. preopen) in (X,r.s), where rs denotes the semi-regularization of r. By using this fact, we can obtain several new characterizations of s-closed spaces, semi-connected spaces, and some separation axioms.
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