Almost closed linear subspaces of strict inductive limits of sequences of Fréchet spaces

Sufficient conditions are given for the existence, in the strict inductive limit of an increasing ing sequence of Fréchet spaces, of nonclosed linear subspaces whose traces on the defining spaces are closed. These conditions are satisfied, in particular, by the Schwartz space of infinitely differentiable functions with compact support on finite-dimensional Euclidean space.
References: 12 titles.