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.
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.
Abstract
We show functoriality of γα in our joint paper with Á. Császár “Further remarks on δ- and θ-modifications”.
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.
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
Abstract
We introduce the notion of mixed weak (μ,ν1ν2)-continuity between a generalized topology μ and two generalized topologies ν1, ν2. We characterize such continuity in terms of mixed generalized open sets: (ν1,ν2)′-semiopen sets, (ν1,ν2)′-preopen sets, (ν1,ν2)-preopen sets [2], (ν1,ν2)′-β′-open sets and θ(ν1,ν2)-open sets [3]. In particular, we show that for a given mixed weakly (μ,ν1ν2)-continuous function, if the codomain of the given function is mixed regular (=(ν1,ν2)-regular), then the function is also (μ,ν1)-continuous.
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.
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.
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.
Abstract
We introduce the notion of strongly-
-locally closed sets to obtain decompositions of ∗-continuity.
