## Linear Operators, Part 1 |

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Page 8

Hence, by Theorem 7, there is a maximal well-ordered

E for if a. is in E but not in Eo the ordering so in Eo may be extended to the set Eo

U (r} by defining y <o a for ge Eo. Q.E.D. 3. Exercises 1 If (E, s) is a p.o.s. with ...

Hence, by Theorem 7, there is a maximal well-ordered

**subset**Eo of E. Now Eo =E for if a. is in E but not in Eo the ordering so in Eo may be extended to the set Eo

U (r} by defining y <o a for ge Eo. Q.E.D. 3. Exercises 1 If (E, s) is a p.o.s. with ...

Page 440

totally ordered subfamily of .2/, the non-void set O.2/, is a closed extremal

of K which furnishes a lower bound for ...'. It follows by Zorn's lemma that .2/

contains a minimal element Ao. Suppose that Ao contains two distinct points p

and q.

totally ordered subfamily of .2/, the non-void set O.2/, is a closed extremal

**subset**of K which furnishes a lower bound for ...'. It follows by Zorn's lemma that .2/

contains a minimal element Ao. Suppose that Ao contains two distinct points p

and q.

Page 456

(Schauder-Tychonoff) A compact conver

topological space has the fired point property. PRoof. By Zorn's lemma there

exists a minimal convex

previous ...

(Schauder-Tychonoff) A compact conver

**subset**of a locally conver lineartopological space has the fired point property. PRoof. By Zorn's lemma there

exists a minimal convex

**subset**Kı of K with the property that TK C K1. By theprevious ...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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