## Convex sets |

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### Contents

PREFACE | 1 |

P A R T 11 Hyperplanes and the Separation Theorem | 19 |

The Minkowski Metric | 31 |

Copyright | |

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### Common terms and phrases

bd conv Blaschke bounded closed C-convex closed connected set closed convex set closed half-spaces closed set common transversal compact convex body compact convex set compact set complete the proof Condition connected set contains at least convex cone convex functional convex hull convex polyhedron core countable dimension disjoint dual cone end point euclidean space Exercise exists a neighborhood exists a point extreme point finite number finite-dimensional following theorem half-spaces Helly's theorem Hence hyperplane H implies there exists inner-product space int conv interior intv xy Klee Lemma line segment linear functional Math maximal convex subsets members of SF metric space Minkowski space Ln n-dimensional nonempty intersection normed linear space open set plane of support point in common polyhedra Problem proof of Theorem Proposition prove radius simplex solid circle solid sphere subspace support functional Suppose topological linear space topological space Valentine vertex vertices