半凸性与Fuzzy拓扑线性空间

Semi—Convexity and Fuzzy Topological Linear Space

本文引进了半凸fu=y集和局部半凸fu=y拓扑线性空间的概念,研究了它们的某些性质,借助于fu=y拟 p_■—范族(a∈Г.0<p_■≤1)给出了fu=y拓扑线性空间为局部半凸的一个充分必要条件。

In this paper,we first introduce the notions of semi—convex fuzzy set and locally semi—convex fuzzy topological linear space,and then study some of their properties.Finally We give a nec-essary and sufficient condition,by means of a family of fuzzy p_a—pseudonorms(u∈(?),0<p_a≤1),for a fuzzy topological linear space to be locally semi—convex.