# Regular inductive limits of K-spaces.

Collectanea Mathematica (1991)

- Volume: 42, Issue: 1, page 45-49
- ISSN: 0010-0757

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topGilsdorf, 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 -

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