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localy convex space; webbed space; sequential completeness; regularity of an inductive limit
Any inductive limit of bornivorously webbed spaces is sequentially complete iff it is regular.
[1] M.  De Wilde: Closed Graph Theorem and Webbed Spaces. Pitman, 1978.
[2] G. Köthe: Topological Vector Spaces II. Springer-Verlag, 1979. MR 0551623
[3] W.  Robertson: On the closed graph theorem with webs. Proc. London Math. Soc. 24 (1972), 692–738. MR 0306857
[4] J. Kučera, C. Bosch: Bounded sets in fast complete inductive limits. Internat J.  Math. 7 (1984), 615–617. DOI 10.1155/S016117128400065X | MR 0771609
[5] J. Kučera: Sequential completeness of $LF$-spaces. Czechoslovak Math.  J 51 (2001), 181–183. DOI 10.1023/A:1013722325291 | MR 1814643
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