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Journal of Convex Analysis 10 (2003), No. 1, 109--127
Copyright Heldermann Verlag 2003

Positively Convex Modules and Ordered Normed Linear Spaces

Dieter Pumplün
Fachbereich Mathematik, Fernuniversität, 58084 Hagen, Germany,

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.

MSC 2000: 52A05, 52A01, 46B40, 46A55.

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