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.
The concept of θ(g, g′)-continuity was introduced by Császár . 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.
The notions of δ(μ1,μ2), θ(μ1,μ2) and (θ(μ1,μ2),θ(σ1,σ2))-continuity were introduced in . In this paper, the characterization of the continuity is investigated, and we introduce the (δ(μ1,μ2),δ(σ1,σ2))-continuity on generalized topological spaces. Finally, we investigate the relations between (θ(μ1,μ2),θ(σ1,σ2))-continuity and (δ(μ1,μ2),δ(σ1,σ2))-continuity on generalized topological spaces
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 , (ν1,ν2)′-β′-open sets and θ(ν1,ν2)-open sets . 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.
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
Characterizations of some properties of generalized R0 and R1 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.