METRIZABLE BARRELLED COUNTABLE ENLARGEMENTS

Abstract

In 1980, Robertson, Tweddle and Yeomans solved the metrizable BCE problem in certain special cases, for example, in the normable case under assumption of the Continuum Hypothesis (CH). A complete positive solution was recently given by the author and L. M. Sánchez Ruiz under an assumption, weaker than CH, that scales exist. A better partial solution for the general BCE problem obviates scales or other extra-ZFC assumptions, and entirely lays to rest the metrizable BCE problem. The proof stimulates thought about how the least infinite-dimensionality of normed barrelled spaces impinges on the separable quotient problem for Banach spaces.