## Linear Operators, Part 1 |

### From inside the book

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Page 18

A continuous one-to-one map from a

homeomorphism. PRoof. Let X be a

one-to-one continuous function on X, with f(X) = Y. According to the preceding ...

A continuous one-to-one map from a

**compact**space to a**Hausdorff space**is ahomeomorphism. PRoof. Let X be a

**compact**space, Y a**Hausdorff space**, and f aone-to-one continuous function on X, with f(X) = Y. According to the preceding ...

Page 276

Suppose, in addition to the hypotheses of Theorem 18, that the functions of QI

distinguish between the points of S. Then there easists a

each f in ...

Suppose, in addition to the hypotheses of Theorem 18, that the functions of QI

distinguish between the points of S. Then there easists a

**compact Hausdorff****space**S, and a one-to-one embedding of S as a dense subset of S, such thateach f in ...

Page 516

39 Let S be a

Show that there is a regular countably additive non-negative measure u defined

for all Borel sets in S with the properties that u is not identically zero and u is ...

39 Let S be a

**compact Hausdorff space**and d a continuous function on S to S.Show that there is a regular countably additive non-negative measure u defined

for all Borel sets in S with the properties that u is not identically zero and u is ...

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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

### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero