Geodesic
Sequential retractivities and regularity on inductive limits
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 847-851.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper we prove the following result: an inductive limit $(E,t) = \text{ind}(E_n,t_n)$ is regular if and only if for each Mackey null sequence $(x_k)$ in $(E,t)$ there exists $n=n(x_k)\in \mathbb N$ such that $(x_k)$ is contained and bounded in $(E_n,t_n)$. From this we obtain a number of equivalent descriptions of regularity.
Classification : 46A13, 46M40
Keywords: inductive limits; regularity; sequential retractivities 
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     author = {Jing-Hui, Qiu},
     title = {Sequential retractivities and regularity on inductive limits},
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Jing-Hui, Qiu. Sequential retractivities and regularity on inductive limits. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 847-851. http://geodesic.mathdoc.fr/item/CMJ_2000__50_4_a11/