Abstract

A positively convex module is a non-empty set closed under positively convex combinations but not necessarily a subset of a linear space. Positively convex modules are a natural generalization of positively convex subsets of linear spaces. Any positively convex module has a canonical semimetric and there is a universal positively affine mapping into a regularly ordered normed linear space and a universal completion

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Mathematics Subject Classification

52A05, 52A01, 46B40, 46A55

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Suggested citation

D. Pumplün. “Positively Convex Modules and Ordered Normed Linear Spaces.” Journal of Convex Analysis 10 (2003), No. 1, 109–127. https://doi.org/10.68381/jca1005

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Published by Heldermann Verlag, 2003. Rights now held by Banach Press LLC.