Regular inductive limits of K-spaces.
Gilsdorf, Thomas E.
Collectanea Mathematica, Tome 42 (1991), p. 45-49 / Harvested from Biblioteca Digital de Matemáticas

A well-known result for bounded sets in inductive limits of locally convex spaces is the following: If each of the constituent spaces En are Fréchet spaces and E is the inductive limit of the spaces En, then each bounded subset of E is bounded in some En iff E is locally complete. Using DeWilde's localization theorem, we show here that the completeness of each En and the local completeness of E may be replaced with the conditions that the spaces En are all webbed K-spaces and E is locally Baire, respectively.

Publié le : 1991-01-01
DMLE-ID : 488
@article{urn:eudml:doc:42437,
     title = {Regular inductive limits of K-spaces.},
     journal = {Collectanea Mathematica},
     volume = {42},
     year = {1991},
     pages = {45-49},
     zbl = {0772.46001},
     mrnumber = {MR1181061},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42437}
}
Gilsdorf, Thomas E. Regular inductive limits of K-spaces.. Collectanea Mathematica, Tome 42 (1991) pp. 45-49. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42437/