Fuzzy Topology Induced By Strong Fuzzy Norms

The theory of fuzzy normed linear space is an important part of fuzzy anal-ysis. The topological structure in fuzzy normed spaces has been the focus of many scholars. Based on the strong fuzzy metric space,this thesis makes a de-tailed study on the fuzzifying topology in strong fuzzy normed linear spaces.The main contents are as follows:Firstly, the concept of strong fuzzy normed linear space is introduced, and the family of classical topologies with stratified structure in strongly fuzzy normed space is given. The fuzzifying topology in strong fuzzy normed spaces is determined by using the family of ordinary topologies. The compatibility of fuzzifying topology and linear operation is proved. In this thesis, we give the notion of convergence degree for sequences with the characterization of fuzzy norm in the strong fuzzy normed linear spaces. Another proof of the compatibility of the fuzzifyng topology and linear operation is obtained. We also studied the continuity of mappings in strong fuzzy normed linear spaces.Secondly, we give two definitions of the product fuzzy norm of finite fuzzy normed linear spaces, and prove the topological equivalence of this two kind-s of the product fuzzy norm. The definition of a countable of fuzzy normed linear space products is given and the topological structure is studied. Specifi-cally, we proved the fuzzifying product topology of finite strong fuzzy normed spaces is equal to the product of its factor spaces. And we prove the fuzzify-ing product topology of a countable strong fuzzy normative product spaces is stronger than the product of its factor spaces.