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Abstract  

We introduce the notion of almost (g, g′)-continuous functions on GTS’s and investigate properties of such functions and relationships among (g, g′)-continuity, almost (g, g′)-continuity and weak (g, g′)-continuity.

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Abstract  

The concept of θ(g, g′)-continuity was introduced by Császár [1]. In this paper, we investigate characterizations for θ(g, g′)-continuous functions and introduce the concept of weak θ(g, g′)-continuity, and study characterizations for weak θ(g, g′)-continuity and the relationships among θ(g, g′)-continuity, weak (g, g′)-continuity and weak θ(g, g′)-continuity.

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Abstract  

We show functoriality of γα in our joint paper with Á. Császár “Further remarks on δ- and θ-modifications”.

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Abstract

We introduce a new notion called contra-(μ,λ)-continuous functions as functions on generalized topological spaces [8]. We obtain some characterizations and several properties of such functions. The functions enable us to formulate a unified theory of several modifications of contra-continuity due to Dontchev [18].

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Abstract

We further extend the study of weak structures and m-structures defined on a set X and prove that an m-structure generates a finer topology.

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Abstract  

We introduce the notions of weak (g, g′)-continuity and weak (ψ, ψ′)-continuity on GTS’s and GNS’s, respectively, and investigate characterizations for such functions and relationships between weak (g, g′)-continuity and weak (ψ, ψ′)-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 the notion of mixed weak (μ1ν2)-continuity between a generalized topology μ and two generalized topologies ν1, ν2. We characterize such continuity in terms of mixed generalized open sets: (ν12)′-semiopen sets, (ν12)′-preopen sets, (ν12)-preopen sets [2], (ν12)′-β′-open sets and θ12)-open sets [3]. In particular, we show that for a given mixed weakly (μ1ν2)-continuous function, if the codomain of the given function is mixed regular (=(ν12)-regular), then the function is also (μ1)-continuous.

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Abstract

We introduce the so-called g-α-irresolute functions in generalized topological spaces. We obtain some properties and several characterizations of this type of functions.

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Abstract  

We characterize δ-I-sets, discuss the relation between δ-sets, δ-I-sets and I δ-sets and generalize some of the results.

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