## Linear Operators: General theory |

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Page 8

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

= E for if x is in E but not in E , the ... 2 If a family & of

property that A E E if and only if every finite

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

**subset**E , of E . Now E ,= E for if x is in E but not in E , the ... 2 If a family & of

**subsets**of a set has theproperty that A E E if and only if every finite

**subset**of A belongs to E , then E ...Page 17

A real continuous function defined on a closed

real continuous extension defined on the whole space . Proof . The only case

where the theorem does not apply immediately is the case where f is unbounded

.

A real continuous function defined on a closed

**subset**of a normal space has areal continuous extension defined on the whole space . Proof . The only case

where the theorem does not apply immediately is the case where f is unbounded

.

Page 456

( Schauder - Tychonoff ) A compact convex

topological space has the fixed point property . Proof . By Zorn ' s lemma there

exists a minimal convex

previous ...

( Schauder - Tychonoff ) A compact convex

**subset**of a locally convex lineartopological space has the fixed point property . Proof . By Zorn ' s lemma there

exists a minimal convex

**subset**K , of K with the property that TK , CK . By theprevious ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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