## Linear Operators: General theory |

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Page 410

1 Definition. A

The following lemma is an obvious consequence of Definition 1. 2 Lemma. The

intersection of an arbitrary family of

1 Definition. A

**set**K Q X is**convex**ifx,ye K, and 0 ^ a ^ 1, imply ax-\-(l — a)y e K.The following lemma is an obvious consequence of Definition 1. 2 Lemma. The

intersection of an arbitrary family of

**convex**subsets of the linear space X is**convex**.Page 461

and an arbitrary

Theorem 2.8). He also proved that a

topology of the normed linear space 3£, can be separated from an arbitrary

closed ...

and an arbitrary

**convex set**is possible, provided they are disjoint (compareTheorem 2.8). He also proved that a

**convex set**K which is compact in the 36*topology of the normed linear space 3£, can be separated from an arbitrary

closed ...

Page 842

See also Convex hull,

10.1 (520) study of, VI. 10 Convex hull, V.2.2 (414)

definition, V.l.l (410) study of, V.l-2 Convex space, locally, V.2.9 (417), (471 )

strictly, ...

See also Convex hull,

**Convex set**. Convex space) Convex function, definition, VI.10.1 (520) study of, VI. 10 Convex hull, V.2.2 (414)

**Convex set**, II.4.1 (70)definition, V.l.l (410) study of, V.l-2 Convex space, locally, V.2.9 (417), (471 )

strictly, ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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