## Linear Operators: General theory |

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Page 10

A

a point p is a Ziwu'< point, or a poin< o/ accumulation, of .4 provided every

in X ...

A

**neighborhood**of the set A is an open set containing A. If A is a subset of X, thena point p is a Ziwu'< point, or a poin< o/ accumulation, of .4 provided every

**neighborhood**of p contains at least one point q p, with q e A. The interior of a setin X ...

Page 51

Let the homomorphism / : G -> H be continuous at x, and let y e G. If V is a

is a

such ...

Let the homomorphism / : G -> H be continuous at x, and let y e G. If V is a

**neighborhood**of f(y), then, by Lemma 2(c), Vf(y~1x) is a**neighborhood**of f(x). If Uis a

**neighborhood**of a: such that f{V)Q Vf(y~1x), then Ux^y is a**neighborhood**of ysuch ...

Page 56

of the image of any

b, there is a

and so x e ...

of the image of any

**neighborhood**G of the element 0 in £ contains a**neighborhood**of the element 0 in 3). Since a—b is a continuous function of a andb, there is a

**neighborhood**M of 0 such that M—MQG. For every x e X, x/n -*□ 0,and so x e ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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