## Linear Operators: General theory |

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Page 21

A set is said to be

nowhere

, if it contains a denumer- able

A set is said to be

**dense**in a topological space X, if its closure is X. It is said to benowhere

**dense**if its closure does not contain any open set. A space is separable, if it contains a denumer- able

**dense**set. 12 Theorem. // a topological space ...Page 451

We wish to prove that Z = Z„ = flti Zn ( is

in X, and that p 4 Z. Then some sphere S(p, e) does not intersect Z. If S = S(p, e/2)

, then SZ = <f>. Hence U"_x -SZ„ , = 5. It follows from Theorem 1.6.9 that some ...

We wish to prove that Z = Z„ = flti Zn ( is

**dense**in X. Suppose that Z is not**dense**in X, and that p 4 Z. Then some sphere S(p, e) does not intersect Z. If S = S(p, e/2)

, then SZ = <f>. Hence U"_x -SZ„ , = 5. It follows from Theorem 1.6.9 that some ...

Page 842

4.14 (182) Saks decomposition, IV.9.7 (308) Yosida-Hewitt decomposition, (233)

De Morgan, rules of, (2)

V.7.40-^1 (488-439)

4.14 (182) Saks decomposition, IV.9.7 (308) Yosida-Hewitt decomposition, (233)

De Morgan, rules of, (2)

**Dense**convex sets, V.7.27 (437)**Dense**linear manifolds,V.7.40-^1 (488-439)

**Dense**set, definition, 1.6.11 (21) density of simple ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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