L-Fuzzy N-compact Quotient Mapping And L-Fuzzy N-compact Quotient Topology

In this paper, it was consisted of two independent main elements:Firstly, L - fuzzyN-compact quotient order-homomorphism and L - fuzzy N-compact quotient topology. Secondly , strong uncertainty mapping, strong semi-continuous mapping. Now the brief summary of the contents of the two pieces of essays is as follows:1. L - fuzzy N-compact quotient-mapping and L - fuzzy N-compact quotient topologyIn the L - fuzzy topological spaces, N-compact is a topological important concept. It is a good extension of compactness. Paper [3] gives the compactness quotient mapping and compactness quotient topology, and study a series of their properties within the range of general topology. But in my paper, we define L -fuzzy N-compact quotient mapping and L -fuzzy N-compact quotient topology by using of the N-compactness, extend paper [3] successfully to L - Fuzzytopology. N-compactness is not copied form in the concept of compactness. The concept of N-compact, but rather than the concept of compactness, is more complicated and more profound, so our works are a meaningful extension.2. strong uncertainty mapping, strong semi-open open mapping and strong semi-continuous mapping Follow the semi-open set, many scholars pay attention to strong semi-open set. For example, HouYuan Li has studied the topological properties of semi-open subsets andα? sets [4,5] , GuangJi Zhang has studied the properties of the coverage of strong semi-open sets[6]etc. This paper, we define strong uncertainty mapping, strong semi-open open mapping and strong semi-continuous mapping by using strong semi-open sets, further study its relationship and properties between them.