Fuzzy C. T Yang's Theorem In Topological Spaces And Metrization

The dissertation is divided into five chapters.I have done the following fouraspects work. First, two kinds of adherence point and accumulation point, arecompared and analysed, one is defined by M.MachoStadler and M.A.de PradaVicente,the other is defined by Zike Deng, some new results and theorems are alsoobtained. Second, C ?Th Yang theorem is investigated in Fuzzy Topological space,and some new results are also obtained ~Third, we generalize and investigate theProduct Induced Fts defined by Hu Cheng-ming. We obtain some new extendedproperties. A new fixed-point theorem is obtained in fuzzy topology space. Fourth,in this chapter, we prove that two kinds of definitions of metrization are equal, one isfrom Deng Zike, the other is from Hu Cheng-ming, According to this result,we get asufficient condition for metrizability of a fuzzy space, which is that if Fts (X, c5)is 13 and has a ?fuzzy locally finite base, it is metrizable. This result greatlyimproves Zike DENG `s result about metrization. At the same time, we also obtainsome new results.