## Convex Sets |

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### Contents

PRE FACE IV | 1 |

Hyperplanes and the Separation Theorem | 19 |

1 The Minkowski Metric | 31 |

Copyright | |

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### Common terms and phrases

assume Banach space boundary bounded called Choose circle clearly closed convex closed set collection common compact convex body compact set complete Condition cone connected set Consider constant contains continuous contradiction conv convergence convex sets cony core corresponding curve defined Definition denote determined dimension disjoint element euclidean Exercise exists a point extreme fact Figure finite flat following theorem functional given half-spaces Hence holds implies interior intersection intv Klee least Lemma locally convex Math maximal convex subsets members of F neighborhood nonempty normed linear space open set parallel plane Problem Proof Proposition prove radius relative Remark respectively result satisfies segment separates solid sphere space L star-shaped Suppose surface Theorem topological linear space translate union Valentine vertices