Displaying similar documents to “Strictly barrelled disks in inductive limits of quasi-(LB)-spaces.”

Regular inductive limits of K-spaces.

Thomas E. Gilsdorf (1991)

Collectanea Mathematica

Similarity:

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...

Some examples on quasi-barrelled spaces

Manuel Valdivia (1972)

Annales de l'institut Fourier

Similarity:

The three following examples are given: a bornological space containing a subspace of infinite countable codimension which is not quasi-barrelled, a quasi-barrelled 𝒟 ℱ -space containing a subspace of infinite countable codimension which is not 𝒟 ℱ -space, and bornological barrelled space which is not inductive limit of Baire space.