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Uniform maps into normed spaces

Zdeněk Frolìk (1974)

Annales de l'institut Fourier

Thirteen properties of uniform spaces are shown to be equivalent. The most important properties seem to be those related to modules of uniformly continuous mappings into normed spaces, and to partitions of unity.

Unitary sequences and classes of barrelledness.

Manuel López Pellicer, Salvador Moll (2003)

RACSAM

It is well known that some dense subspaces of a barrelled space could be not barrelled. Here we prove that dense subspaces of l∞ (Ω, X) are barrelled (unordered Baire-like or p?barrelled) spaces if they have ?enough? subspaces with the considered barrelledness property and if the normed space X has this barrelledness property.These dense subspaces are used in measure theory and its barrelledness is related with some sequences of unitary vectors.

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