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In this chapter we give a completely general theory of decomposition of nonpointed non-closed convex cones, removing the condition that the lineality space be closed. Thus we assume that neither the cone nor its lineality space be closed. This condition is instrumental to prove a general support condition for void interior closed sets, which does not assume that the support point be extreme.

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A Completely General Decomposition of Cones and a Support Condition

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  • 发表日期：

    2025年

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  • Paolo d’Alessandro

摘要

In this chapter we give a completely general theory of decomposition of nonpointed non-closed convex cones, removing the condition that the lineality space be closed. Thus we assume that neither the cone nor its lineality space be closed. This condition is instrumental to prove a general support condition for void interior closed sets, which does not assume that the support point be extreme.