The Hahn–Banach Theorem for Partially Ordered Totally Convex, Positively Convex and Superconvex Modules |
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Authors: | Stefan Nörtemann |
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Affiliation: | (1) Parkallee 30 M, 44866 Bochum, Germany |
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Abstract: | The Hahn–Banach Theorem for partially ordered totally convex modules [3] and a necessary and sufficient condition for the existence of an extension of a morphism from a submodule C0 of a partially ordered totally convex module C (with the ordered unit ball of the reals as codomain) to C, are proved. Moreover, the categories of partially ordered positively convex and superconvex modules are introduced and for both categories the Hahn–Banach Theorem is proved. |
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Keywords: | Hahn– Banach Theorem partially ordered totally convex module partially ordered positively convex module partially ordered superconvex module |
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