In this paper we deal with a concrete example of a generalized topological space and we shall examine some topological properties such as, the usual continuity, the net-continuity and the net-closure property for it. We will show that a generalized topological space has net-continuous property or net-closure property if and only if it is a topological space. Finally we give examples of continuo...

We introduce a topological graph parameter σ(G), defined for any graph G. This parameter characterizes subgraphs of paths, outerplanar graphs, planar graphs, and graphs that have a flat embedding as those graphs G with σ(G) ≤ 1, 2, 3, and 4, respectively. Among several other theorems, we show that if H is a minor of G, then σ(H) ≤ σ(G), that σ(Kn) = n−1, and that if H is the suspension of G, th...

A topological property is properly hereditary property if whenever every proper subspace has the property, the whole space has the property. In this note, we will study some topological properties that are preserved by proper subspaces; in fact, we will study the following topological properties: Baire spaces, second category, sequentially compact, hemicompact, δ-normal, and spaces having dispe...

It is proved that any molecular graph invariant (that is any topological index) can be uniquely represented as (1) a linear combination of occurrence numbers of some substructures (fragments), both connected and disconnected, or (2) a polynomial on occurrence numbers of connected substructures of corresponding molecular graph. Besides, any (0,l)-valued molecular graph invariant can be uniquely ...

This paper deals with the delimitation of the power of local computations on graphs having some initial knowledge, e.g. the size or the topology of the network. We refine a proof technique based on coverings in order to cope with additional knowledge. Applying this method we show that several graph properties (e.g., planarity) are not recognizable even if some simple knowledge about the graph (...

In this paper, by using C-sequentially sign property for bifunctions, we provide sufficient conditions that ensure the existence of solutions of some vector equilibrium problems in Hausdorff topological vector spaces which ordered by a cone. The conditions which we consider are not imposed on the whole domain of the operators involved, but just on a locally segment-dense subset of the domain.

n this paper, we consider continuity properties(especially, regularity, also viewed as an approximation property) for $%mathcal{p}_{0}(x)$-valued set multifunctions ($x$ being a linear,topological space), in order to obtain egoroff and lusin type theorems forset multifunctions in the vietoris hypertopology. some mathematicalapplications are established and several physical implications of thema...