In recent years, models of spatial relations have attracted much attention from GIS community, especially topological relations. In this paper, some basic topologic models for spatial entities in both vector and raster spaces are discussed. To make the concepts more formalized, some new concepts from a new branch of mathematics -pansystems -are adopted. In doing so, the basic concepts of pansys...

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...

In a first course in functional analysis, a great deal of time is spent with Banach spaces, especially the interaction between such spaces and their dual spaces. Banach spaces are a special type of topological vector space, and there are important topological vector spaces which do not lie in the Banach category, such as the Schwartz spaces. The most fundamental theorem about Banach spaces is t...

Let a topological space. An intersection graph on a topological space , which denoted by ‎ , is an undirected graph which whose vertices are open subsets of and two vertices are adjacent if the intersection of them are nonempty. In this paper, the relation between topological properties of  and graph properties of ‎  are investigated. Also some classifications and representations for the graph ...

in this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. we also investigate effect to fuzzy soft connectedness. moreover, c_i-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

The line density of line defects in terms of a two-component vector order parameter are obtained from the definition of topological charges of line defects. The spatial structure and bifurcation of line defects in three-dimensional space are also studied from the topological properties of the two-component vector order parameter. The branch conditions for generating, annihilating, colliding, sp...

In this paper, we consider strong form of a vector equilibrium problem and establish some existence results for solutions of such problem in the setting of topological vector spaces. We provide several coercivity conditions under which strong vector equilibrium problem has a solution. Our results generalize and extend the results of Bianchi and Pini [Coercivity conditions for equilibrium proble...