## Linear Operators: General theory |

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Page 18

A continuous one-to-one map from a

homeomorphism. Proof. Let AT 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 AT be a

**compact**space, Y a**Hausdorff space**, and / 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 91

distinguish between the points of S. Then there exists a

Sx and a one-to-one embedding of S as a dense subset of S1 such that each f in

...

Suppose, in addition to the hypotheses of Theorem 18, that the functions of 91

distinguish between the points of S. Then there exists a

**compact Hausdorff space**Sx and a one-to-one embedding of S as a dense subset of S1 such that each f in

...

Page 516

39 Let S be a

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

for all Borel sets in S with the properties that fi is not identically zero and /j, ...

39 Let S be a

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

for all Borel sets in S with the properties that fi is not identically zero and /j, ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

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### Common terms and phrases

Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero