L-模糊赋范空间的完备化

On the Completion of L-fuzzy normed spaces

本文探讨L-模糊赋范空间的完备化问题.首先给出L-模糊赋范空间中L-模糊点列的柯西列和完备空间的概念,然后定义了两个L-模糊赋范空间之间的等距同构以及LX中层层一致稠密的集合,最后证明了每个L-模糊赋范空间在等距同构意义下有唯一的完备L-模糊赋范空间.

This paper discusses the completion of L-fuzzy normed spaces. Firstly, the notions of Cauchy sequence and the completeness in L-fuzzy normed spaces are introduced. Subsequently, we give the concepts of isometric isomorphism between two L-fuzzy normed spaces and the uniformly dense sets for all stratum in L^X, by which we characterize the completion of L-fuzzy normed space. Finally, we prove that the completion of each L-fuzzy normed space exists and its completion is unique up to isometric isomorphism.