Separation axioms on enlargements of generalized topologies

On generalized topological molecular lattices

In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices,  topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and defi...

L-pre-separation axioms in (2, L)-topologies based on complete residuated lattice-valued logic

In the present paper we introduce and study L-pre-T0-, L-pre-T1-, L-pre-T2 (L-pre-Hausdorff)-, L-pre-T3 (L-preregularity)-, L-pre-T4 (L-pre-normality)-, L-pre-strong-T3-, L-pre-strong-T4-, L-pre-R0-, L-pre-R1-separation axioms in (2, L)-topologies where L is a complete residuated lattice. Sometimes we need more conditions on L such as the completely distributive law or that the ”∧” is distribut...

On generalized topologies arising from mappings

Given a mapping $f:Xto X$ we naturally associate to it a monotonic map $gg_f:exp Xto exp X$ from the power set of $X$ into itself, thus inducing a generalized topology on $X$. In this paper we investigate some properties of generalized topologies which are defined by such a procedure.

On bD-Sets and Associated Separation Axioms

On Density Topologies with Respect to Invariant Σ-ideals

The density topologies with respect to measure and category are motivation to consider the density topologies with respect to invariant σ-ideals on R. The properties of such topologies, including the separation axioms, are studied.