The present note investigates the closed hull of subsets
M contained in the (unrestricted) inductive limit
E[τ] of topological vector spaces
Eα[τ
α], α∈A. Sufficient conditions for the validity of \bar{
M}
τ=∪\limits
α∈A\overline{M∩
Eατα} are given. These conditions are discussed by examples, and it is shown that there is not any redundance among them. Applications to F-linked topologies and sequence spaces are indicated. Futhermore, some inaccuracies contained in some of the standard text books are corrected.
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