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Any LF-space is sequentially complete iff it is regular.
A notion of an almost regular inductive limits is introduced. Every sequentially complete inductive limit of arbitrary locally convex spaces is almost regular.
In this note, we investigate non-locally-convex topological vector spaces for which the closed graph theorem holds. In doing so, we introduce new classes of topological vector spaces. Our study includes a direct extension of Pták duality to the non-locally-convex situation.
Certain classes of locally convex space having non complete separated quotients are studied and consequently results about -completeness are obtained. In particular the space of L. Schwartz is not -complete where denotes a non-empty open set of the euclidean space .
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