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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  

A quasi-topology is a generalized topology (cf. [3]) closed for finite intersections. The paper discusses the question whether statements valid for topologies can be generalized for quasi-topologies.

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Abstract

The notions of δ(μ 1,μ 2), θ(μ 1,μ 2) and (θ(μ 1,μ 2),θ(σ 1,σ 2))-continuity were introduced in [2]. In this paper, the characterization of the continuity is investigated, and we introduce the (δ(μ 1,μ 2),δ(σ 1,σ 2))-continuity on generalized topological spaces. Finally, we investigate the relations between (θ(μ 1,μ 2),θ(σ 1,σ 2))-continuity and (δ(μ 1,μ 2),δ(σ 1,σ 2))-continuity on generalized topological spaces

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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  

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  

Characterizations of some properties of generalized R 0 and R 1 topological spaces by using closure operator defined on a generalized topological space will be given. It is also shown that many results done in this area in some previous papers can be considered as special cases of our results.

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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 notion of strongly--locally closed sets to obtain decompositions of ∗-continuity.

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