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. 1991 Mathematics Subject Classification 46A08.

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