Some properties of fuzzy metric spaces

被引：198

作者：

Gregori, V

Romaguera, S ^{[1
]}

机构：

[1] Univ Politecn Valencia, Dept Matemat Aplicada, Escuela Caminos, E-46071 Valencia, Spain

[2] Univ Politecn Valencia, Escuela Univ Gandia, Valencia, Spain

来源：

FUZZY SETS AND SYSTEMS | 2000年 / 115卷 / 03期

关键词：

topology; fuzzy metric space; complete; compact; precompact;

D O I：

10.1016/S0165-0114(98)00281-4

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We prove that the topology induced by any (complete) fuzzy metric space (in the sense of George and Veeramani) is (completely) metrizable. We also show that every separable fuzzy metric space admits a precompact fuzzy metric and that a fuzzy metric space is compact if and only if it is precompact and complete. Finally, we generalize, among other classical results, the Niemytzki-Tychonoff theorem to fuzzy metric spaces. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：485 / 489

页数：5

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