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, As nuclear (F)-space are reflexive, and as reflexive spaces are stables by projective limit (proposition 1), a LNDF space is reflexive

. Again, the dual E 1 of a LNF-space E " lim Ý Ñi E i identifies as a linear space to a projective limit of complete nuclear (DF)-spaces. As the limit lim Ý Ñi E i is regular