Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • l∞-barrelled
  • dual locally complete
  • primitive
  • optimal results
  • measurable cardinals
  • countable enlargements

Mathematics Subject Classification

46A08, 46A03; 03E55, 03E65

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Suggested citation

S. A. Saxon, L. M. Sánchez Ruiz. “Reinventing Weak Barrelledness.” Journal of Convex Analysis 24 (2017), No. 3, 707–762. https://doi.org/10.68381/jca24045

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