Journal of Convex Analysis 24 (2017), No. 3, 707--762
Copyright Heldermann Verlag 2017
Reinventing Weak Barrelledness
Stephen A. Saxon
Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, FL 32611, U.S.A.
stephen_saxon@yahoo.com
Luis M. Sánchez Ruiz
ETSID, Dep. de Matemática Aplicada, Universitat Politècnica, 46022 Valencia, Spain
lmsr@mat.upv.es
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.
Keywords: l∞-barrelled, dual locally complete, primitive, optimal results, measurable cardinals, countable enlargements.
MSC: 46A08, 46A03; 03E55, 03E65
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