Fuzzy topological spaces generated by fuzzy norm

vFUZZY TOPOLOGICAL SPACESGENERATED BY FUZZY NORM(M. Sc. Thesis)Mustafa ÖZBEYGAZ UNIVERSITYINSTITUTE OF SCIENCE AND TECHNOLOGYOctober 2007ABSTRACTIn this thesis, we have related fuzzy topological spaces generated by fuzzy norm.The thesis consists of four sections. In the first part the introduction takes place.In the second part it is examined fuzzy set, fuzzy point, fuzzy level set, fuzzy realnumber, fuzzy continuity, fuzzy convergence and fuzzy Hausdorff in order tohelp the more recent parts. In the third part definition of fuzzy normed linearspace is given and te relation between convergent sequence and Cauchysequence in a fuzzy normed linear space is researched. Furthermore, therelation between fuzzy metric and fuzzy norm is proved. In the last part somedefinitions and propositions are given in fuzzy topological spaces generated byfuzzy norm. Some related propositions proved and relations between them arealso given.Science Code : 204.1.132Key Words : Fuzzy set, Fuzzy real number, Fuzzy level set, Fuzzy normedlinearspace, Fuzzy topology.Page Number : 45Adviser : Prof. Dr. Cemil YILDIZ