## Linear Operators, Part 1 |

### From inside the book

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Page 280

That (1)

to show that condition (3) of that theorem

that S may be embedded as a dense subset of a compact Hausdorff space S, ...

That (1)

**implies**(2) can be proved in a manner similar to that used in Theorem 14to show that condition (3) of that theorem

**implies**(4). From Corollary 19 it followsthat S may be embedded as a dense subset of a compact Hausdorff space S, ...

Page 430

We observe first that each of the three conditions

metric topology, for a "(A) is a bounded set of scalars for each aro e &" and we

can apply II.3.20. It is readily seen that (iii)

We observe first that each of the three conditions

**implies**that A is bounded in themetric topology, for a "(A) is a bounded set of scalars for each aro e &" and we

can apply II.3.20. It is readily seen that (iii)

**implies**(ii). The other implications we ...Page 454

To each point p e C there corresponds a unique nearest point N(p) e K. To see

this, note that Lemma IV.4.2

p-k, - inf, .kp —k then {k} converges, say, to qe K. If{k} is another such minimizing

...

To each point p e C there corresponds a unique nearest point N(p) e K. To see

this, note that Lemma IV.4.2

**implies**that if {k, is a sequence in K such that lim, ...p-k, - inf, .kp —k then {k} converges, say, to qe K. If{k} is another such minimizing

...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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