A new definition of locally convex L-topological vector spaces
首发时间:2008-03-17
Abstract:In this paper, a new definition of locally convex L-topological vector spaces is given. The relationship between this new definition and the previous definition of locally convex L-topological vector spaces given by Yan and Fang [L-fuzzy locally convex topological vector spaces, J. Fuzzy Math. 7 (3) (1999) 765-772] is investigated. Moreover, the concept of generalized L-fuzzy semi-norm is introduced. By using a family of generalized L-fuzzy semi-norms, a characterization of the new locally convex L-topological vector spaces is presented.
keywords: L-topological vector spaces Locally convex L-topological vector spaces Generalized L-fuzzy semi-norms.
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局部凸L-拓扑向量空间的新定义
摘要:本文给出了局部凸L-拓扑向量空间的新定义, 研究了这个新定义与严从华和方锦暄给出的定义之间的关系. 此外, 引进了广义L-fuzzy半范数的概念并利用一族广义L-fuzzy半范数刻画了这种新定义的局部凸L-拓扑向量空间.
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