Reinventing Weak Barrelledness

Abstract

[EN] With scores of novel theorems/examples we establish a hierarchy of 16 barrelled-type properties, consolidating decades of work by dozens of authors, defining/motivating/displaying optimal results. We prove our display answers all 4.29 billion interrelational questions at a glance. We solve the countable enlargement problems for separable weak barrelledness, uniformly relax certain Valdivia hypotheses to a characterization, and show that the existence of measurable cardinals depends on which of two hypotheses is optimal for Dierolf¿s dense subspace theorem.