Regular inductive limits of K-spaces.

Gilsdorf, Thomas E.. "Regular inductive limits of K-spaces.." Collectanea Mathematica 42.1 (1991): 45-49. <http://eudml.org/doc/42437>.

@article{Gilsdorf1991,
abstract = {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.},
author = {Gilsdorf, Thomas E.},
journal = {Collectanea Mathematica},
keywords = {Espacios localmente convexos; Espacios de Fréchet; Espacios lineales topológicos; Propiedades topológicas; bounded sets; inductive limits of locally convex spaces; Fréchet spaces; DeWilde's localization theorem; webbed -spaces; locally Baire},
language = {eng},
number = {1},
pages = {45-49},
title = {Regular inductive limits of K-spaces.},
url = {http://eudml.org/doc/42437},
volume = {42},
year = {1991},
}

TY - JOUR
AU - Gilsdorf, Thomas E.
TI - Regular inductive limits of K-spaces.
JO - Collectanea Mathematica
PY - 1991
VL - 42
IS - 1
SP - 45
EP - 49
AB - 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.
LA - eng
KW - Espacios localmente convexos; Espacios de Fréchet; Espacios lineales topológicos; Propiedades topológicas; bounded sets; inductive limits of locally convex spaces; Fréchet spaces; DeWilde's localization theorem; webbed -spaces; locally Baire
UR - http://eudml.org/doc/42437
ER -