| 刘应明.Fuzzy度量化——嵌入理论的一个应用[J].数学研究及应用,1984,4(3):17~21 |
| Fuzzy度量化——嵌入理论的一个应用 |
| Fuzzy Metrization-an Application of Imbedding Theory |
| 投稿时间：1983-07-07 |
| DOI：10.3770/j.issn:1000-341X.1984.03.004 |
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| 基金项目:中国科学院科学基金会的资助. |
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| A fuzzy Pseudo-metric space is called fuzzy metric space iff it is sub-T0 space. Suppose that (X,F) is a fuzzy topological space. Consider a relation ～between ordinary points of X: x～y iff for each λ≠0,xλ∈yλ and yλ∈xλ. The relation～is an equivalent relation. The corresponding fuzzy quotien space is a sub-T0 space and is called the associated sub-T0 space of (X,F). in this paper, we establish the following theorem via fzzzy imbedding theory:Theorem Suppose that (X,F) is a fuzzy topological space with countable topological base. Then (1)(X,F) is fuzzy metrizable iff it is a fuzzy completely regular and sub-T0 space.(2)(X,F) is a fuzzy completely regular space,then its associated sub-T0 space is fuzzy metrizable. |
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