We introduce and study a new class of spaces, namely $beta-$topological vector spaces via $beta-$open sets. The relationships among these spaces with some existing spaces are investigated. In addition, some important and useful characterizations of $beta-$topological vector spaces are provided.  

A recurring task in mathematics, statistics, and computer science is understanding the connectivity information, or equivalently, the topological properties of a given object. For concreteness, we assume the object in question to be a geometric shape, possibly embedded in a high-dimensional space, although that assumption is not necessary for most of the theory. Algebraic topology offers a tool...

In 1997, Fang proposed the concept of boundedness of $L$-fuzzy setsin $L$-topological vector spaces. Since then, this concept has beenwidely accepted and adopted in the literature. In this paper,several characterizations of bounded $L$-fuzzy sets in$L$-topological vector spaces are obtained and some properties ofbounded $L$-fuzzy sets are investigated.

The main purpose of this paper is to introduce the compatibility of $M$-fuzzifying topologies and $M$-fuzzifying convexities, define an $M$-fuzzifying topological convex space, and give a method to generate an $M$-fuzzifying topological convex space. Some characterizations of $M$-fuzzifying topological convex spaces are presented. Finally, the notion of $M$-fuzzifying weak topologies is obtaine...

let s be a semigroup. in certain cases we give some characterizations of extreme amenability of s and we show that in these cases extreme left amenability and extreme right amenability of s are equivalent. also when s is a compact topological semigroup, we characterize extremely left amenable subalgebras of c(s), where c(s) is the space of all continuous bounded real valued functions on s

Suppose that X is a nonempty subset of a metric space E and Y is a nonempty subset of a topological vector space F. Let g : X → Y and ψ : X ×Y →R be two functions and let S : X → 2Y and T : Y → 2F be two maps. Then the generalized g-quasivariational inequality problem (GgQVI) is to find a point x ∈ X and a point f ∈ T(g(x)) such that g(x) ∈ S(x) and supy∈S(x){Re〈 f , y − g(x)〉 + ψ(x, y)} = ψ(x,...

We define a notion of morphism for quotient vector bundles that yields both a category QVBun and a contravariant global sections functor C : QVBun → Vect whose restriction to trivial vector bundles with fiber F coincides with the contravariant functor Top → Vect of F -valued continuous functions. Based on this we obtain a linear extension of the adjunction between the categories of topological ...