‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra to geometr...

Recently, Huang and Li [J. Li, N.J. Huang, Vector F-implicit complementarity problems in Banach spaces, Appl. Math. Lett. 19 (2006) 464–471] introduced and studied a new class of vector F-implicit complementarity problems and vector F-implicit variational inequality problems in Banach spaces. In this work, we study this class in topological vector spaces and drive some existence theorems for th...

‎By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness...

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...