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| Volume 4, Number 2, May 2008, pp. 293-317 | |||||||||
| Walter Briec and Charles Horvath | |||||||||
| Key words: | |||||||||
| generalized-convexity, B-convexity, Max-Plus convexity, halfspaces, geometric and functional separation, Hahn-Banach like theorems | |||||||||
| Mathematices Subject Classification: 06D50, 32F17 | |||||||||
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| Abstract: | |||
| B-convexity was introduced in [2]. Continuing the investigation initiated in [3] we give complete geometric and analytic characterizations of closed and open B-halfspaces, that is, B-convex sets whose complements are also B-convex. Combined with results of [3] this yields a Hahn-Banach like Theorem in B-convexity which is the exact analog of the usual Hahn-Banach Theorem. Similar results are given in the context of Max-Plus convexity. | |||
| Halfspaces and Hahn-Banach like properties in B-convexity and Max-Plus convexity
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