We give a representation of the completed tensor product $E\;\hat\otimes_{\epsilon_k}\;F$ under certain hypothesis and we obtain a sufficient condition for the topological isomorphism $E\;\hat\otimes_{\epsilon_k}\; (\underrightarrow\lim F_n)\simeq\underrightarrow\lim (E\;\hat\otimes_{\epsilon_k}\; F_n)$.
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