广义模糊p-伪范数与局部半凸I-拓扑向量空间(英文)

Generalized Fuzzy p-Pseudonorm and Locally Semi-Convex I-Topological Vector Spaces

给出局部半凸I-拓扑向量空间的一个新定义,并重新命名"局部半凸模糊拓扑线性空间"为"(QL)-型局部半凸I-拓扑向量空间",研究这两种定义之间的关系,引入广义模糊p-伪范数的概念,证明每个局部半凸I-拓扑向量空间可通过一族广义模糊p-伪范数来刻画.

In this paper, we give a new definition of locally semi-convex I - topological vector spaces and rename locally semi-convex fuzzy topological linear spaces as locally semi-convex I - topological vector spaces of （QL） - type. The relation between these two definitions is studied. We introduce the notion of generalized fuzzy p - pseudonorm, and prove that every locally semi-convex I - vector topology can be determined by a family of generalized fuzzy p - pseudonorms.