The Product Problems On L-fuzzy Topological Spaces With Different Value Ranges

Abstract: In order to study the product of L-fuzzy topological spaces with different value ranges, He Ming introduced the concept of multi-product in [4]. In this paper, the author studies the sufficient and necessary conditions that fuzzy topological properties hold in the multi-product topological space, which include N-compactness, different seperations, cardinal fuctions and induced property. The followings are the main results:(1) Some seperations such as T0 T1 T2 hold in a multi-product topological space if and only if the same seperation still hlods in every factor space.(2) 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 hlods in multi-product fuzzy topological spaces.(3) We study the relation between multi-product fuzzy topological spaces and cardinal fuctions such as weight characteritic density, and so on.(4) Weakly induced property stratification property and induced property are all strongly multiplicative.