## Linear Operators: General theory |

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Page 10

A

then a point p is a limit point , or a point of accumulation , of A provided every

set in ...

A

**neighborhood**of the set A is an open set containing A . If A is a subset of X ,then a point p is a limit point , or a point of accumulation , of A provided every

**neighborhood**of p contains at least one point 9 # p , with q € A . The interior of aset in ...

Page 51

If a homomorphism of one topological group into another is continuous anywhere

, it is continuous . PROOF . Let the homomorphism f : G + H be continuous at x ,

and let y eG . If V is a

...

If a homomorphism of one topological group into another is continuous anywhere

, it is continuous . PROOF . Let the homomorphism f : G + H be continuous at x ,

and let y eG . If V is a

**neighborhood**of f ( y ) , then , by Lemma 2 ( c ) , V / ( y - 1x )...

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 X contains a**neighborhood**of the element 0 in Y . Since a - b is a continuous function of a andb , there is a

**neighborhood**M of 0 such that M - MCG . For every x e X , æ / n + 0 ,and so x e ...

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero