## Convex Sets |

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### Contents

PREFACE | 1 |

Hyperplanes and the Separation Theorem 1 | 19 |

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 convex set compact set complete Condition cone Consider constant contains continuous contradiction conv convex sets cony core corresponding curve Definition denote determined dimension element euclidean Exercise exists exists a point fact Figure finite flat following theorem functional given half-spaces Hence holds hyperplane H 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