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.
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Breckner, W.W., Göpfert, A. & Trif, T. Characterizations of ultrabarrelledness and barrelledness involving the singularities of families of convex mappings. Manuscripta Math 91, 17–34 (1996). https://doi.org/10.1007/BF02567937
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DOI: https://doi.org/10.1007/BF02567937