
In this paper, We discuss the definition of fuzzy subgroup, definition of anti- fuzzy subgroup,the definition of fuzzy normal sub group, definition of anti- fuzzy normal sub group and show the relation between fuzzy normal sub groups and an Anti- fuzzy normal sub groups and derive the definitions of Connectedness and also the definitions of Seperation and derive some theorems on Compactness and Connectedness and define some results on compactness in Fuzzy (anti- fuzzy) sub groups and Fuzzy (anti- fuzzy) normal sub groups.
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