ON 𝜃-MODIFICATIONS OF GENERALIZED TOPOLOGIES VIA HEREDITARY CLASSES

On Generalized Injective Spaces in Generalized Topologies

In this paper, we first present a new type of the concept of open sets by expressing some properties of arbitrary mappings on a power set. With the generalization of the closure spaces in categorical topology, we introduce the generalized topological spaces and the concept of generalized continuity and become familiar with weak and strong structures for generalized topological spaces. Then, int...

On Pre-θ-Open Sets and Two Classes of Functions

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.

Further Remarks on Δ - and Θ - Modifications ∗

In generalizing constructions of N.V. Veli£ko, the paper starts from two generalized topologies μ and μ′ on a set X and introduces two more generalized topologies δ(μ, μ′) and θ(μ, μ′) with the examination of their properties.

Wiener index in weighted graphs via unification of Θ∗Θ∗-classes

It is proved that the Wiener index of a weighted graph (G, w) can be expressed as the sum of the Wiener indices of weighted quotient graphs with respect to an arbitrary combination of Θ∗-classes. Here Θ∗ denotes the transitive closure of the Djoković-Winkler’s relation Θ. A related result for edge-weighted graphs is also given and a class of graphs studied in [19] is characterized as partial cu...