不同值域格值拓扑空间的紧性与分离性

The N-Compactness and Seperations about the Product of L-fuzzy Topological Spaces with Different Value Ranges

讨论了重积空间的紧性和分离性成立的充要条件 .首先 ,对于常见的T0 ,T1 ,T2 等分离性 ,重积空间具有某种分离性当且仅当每个因子空间具有相同的分离性 ,而不需要其他条件 .其次 ,模糊子集的重积是良紧集当且仅当每个模糊子集是良紧集 .从而 ,在重积空间中 ,Ty chonoff乘积定理成立 .

In order to study the product of L-fuzzy topological spaces with different value ranges,He Ming introduced the concept of multi-product. In this paper,the author studies the sufficient and necessary conditions that N-compactness and different seperations hold in the multi-product topological space. Some resluts are revealed:first,some seperation hold in a multi-product topological space if and only if the same seperation still holds in every factor space;secondly,a multi-product of L-fuzzy subsets is N-compact if and only if every L-fuzzy subset is N-compact. Therefore,the Tychonoff Product Theorem holds in the multi-product fuzzy topological spaces.