Dense barrelled subspaces of uncountable codimension. (English) Zbl 0686.46002
Un espace vectoriel topologique séparé E est dit “convenable” s’il possède un sous-espace vectoriel dense M dont la codimension est égale à la dimension de E; il est “convenablement tonnelé” si, en outre, M peut être choisi tonnelé; il est “satisfaisant” si M est dense et tonnelé et si sa codimension est supérieure à la puissance du continu. Ces propriétés, les liens qui existent entre elles, des exemples sont étudiés en détail. Parmi les résultats les plus importants citons: la limite inductive (séparée) d’une suite croissante d’espaces convenablement tonnelés est convenablement tonneĺes; la limite inductive (séparée) d’un système inductif quelconque de db-espaces est convenablement tonneĺe (on rappelle qu’un db-espace est la réunion d’une suite croissante d’espaces vectoriels topologiques, l’un d’entre eux étant à la fois dense et tonnelé).
Reviewer: H.Mascart
MSC:
| 46A08 | Barrelled spaces, bornological spaces |
| 46A13 | Spaces defined by inductive or projective limits (LB, LF, etc.) |
| 46A11 | Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) |
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