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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.

Luis M. Sánchez Ruiz
ETSID, Dep. de Matemática Aplicada, Universitat Politècnica, 46022 Valencia, Spain

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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