非Dedekind完备的序拓扑向量空间中集值映射的一类扩张

在泛函分析中有着重要作用的Hahn-Banach扩张定理及其很多推广定理的条件都要求值域空间是Dedekind完备的,这是一个非常强的条件,因而在一定程度上局限了这些扩张定理的应用。主要考虑弱化这些定理的条件,讨论当值域空间是由锥引入序的非Dedekind完备的序拓扑向量空间时,一类集值映射的扩张。

向量变分不等式与隐向量补问题

研究了序拓扑向量空间拟单调映射对在某些连续条件下的向量隐补问题 。

Inductive Topologies of L-fuzzy Topological Vector Spaces

In this paper, using the theory of L _fuzzy topological vector spaces [1]-[6] , we study some properties of L _fuzzy inductive topologies determined by a family of L _fuzzy linerar order_homomorphisms [2] of L _ftvs, and give a characterization of inductive topologies determined by a single FLOH. As an application of this results, we prove that the quotient space of L _ftvs is also L _ftvs.