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Characterizations of ultrabarrelledness and barrelledness involving the singularities of families of convex mappings
Authors:Wolfgang W Breckner  Alfred Göpfert  Tiberiu Trif
Institution:1. Fac. de Matematic? ?i Informatic?, Universitatea Babe?-Bolyai, Str. Kog?lniceanu Nr. 1, RO-3400, Cluj-Napoca, Romania
2. FB Mathematik und Informatik, Institut für Optimierung und Stochastik, Martin-Luther-Universit?t, D-06099, Halle, Germany
3. Fac. de Matematic? ?i Informatic?, Universitatea Babe?-Bolyai, Str. Kog?lniceanu Nr. 1, RO-3400, Cluj-Napoca, Romania
Abstract:Summary The paper reveals that ultrabarrelled spaces (respectively barrelled spaces) can be characterized by means of the density of the so-called weak singularities of families consisting of continuous convex mappings that are defined on an open absolutely convex set and take values in a locally full ordered topological linear space (respectively locally full ordered locally convex space). The idea to establish such characterizations arose from the observation that, in virtue of well-known results, the density of the singularities of families of continuous linear mappings allows to characterize both the ultrabarrelled spaces and the barrelled spaces.
Keywords:46A08  26B25  52A41
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