Abstract: The concept of relative N-compactness is defined and characterized in terms of nets. It is shown that the relative N-compactness is hereditary with respect to L-fuzzy sets and the relative N-compactness is L-good extension. Some connections between the N-compactness and the relative N-compactness are investigated. It is also proved that induced relative N-compact spaces are productive, and the product of finite relative compact sets is relative compact.

Key words: Fuzzy , topology;Fuzzy ,  set;relative , N-compactness;remote , neighborhood, molecule;net