الفهرس 
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Abstract
it is my duty, as a start to bow my head in true gratitude to Almighty God ,whose guidance, blessing and helps enabled me to take my first step on the path of improving my knowledge through this humble effort. Ihave been extremely fortunate to be supervised in the preparation of This thesis . by professor M.H.Ghanin who introduce me to the world Of fuzzy topology. I wish to express my deeply honest appreciation to him for suggesting the problem, for his continuous encouragement; kind hearted help and valuable discussions. I would like to thank Dr. O.A. Tantawy for his permanent interest, his support during the preparation of this thesis and his valuable discussions. I am very thankful and grateful to Professor R. A. Abd M lateef, (Head of Department of mathematics faculty of science, zagazg university )and all Professors and staff members for their help and support. Finally, i am truly thankful to the great topologist professor A.S. Mashhour who have encouraged me from the beginning.