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• W2528860010 abstract "Let S be a nonvoid set endowed with a ”segment structure“ which generalizes the notion of a segment in a linear space, and which allows to define affine functions. The problem is treated, whether a pair of sets X,Y ⊂ S can be separated by some affine function f : S → R. Here separation means f(y) ≥ f(z), y ∈ Y, z ∈ Z in it’s weakest and infy∈Y f(y) > supz∈Z f(z) in it’s strongest form. Several solutions of this problem are presented as a consequence of von Neumann’s minimax theorem. As special cases we obtain all the classical separation theorems for linear spaces, linear topological spaces, locally convex spaces, normed spaces, etc., but also new results for convex metric spaces are derived." @default.
• W2528860010 created "2016-10-14" @default.
• W2528860010 creator A5013488217 @default.
• W2528860010 date "2000-01-01" @default.
• W2528860010 modified "2023-09-30" @default.
• W2528860010 title "Separation theorems for abstract convex structures" @default.
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• W2528860010 hasPublicationYear "2000" @default.
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