## Linear Operators: General theory |

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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 / 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 21

distinguish between the points of S. Then there exists a

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

Suppose, in addition to the hypotheses of Theorem 18, that the functions of 21

distinguish between the points of S. Then there exists a

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

Page 437

15 If X is a separable linear topological space and A is an X- compact subset of X

*, then the X-topology of A is a metric ... 19 Every normal space S is

homeomorphic to a dense subset S1 of a

every ...

15 If X is a separable linear topological space and A is an X- compact subset of X

*, then the X-topology of A is a metric ... 19 Every normal space S is

homeomorphic to a dense subset S1 of a

**compact Hausdorff space**Cv such thatevery ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations disjoint Doklady Akad Duke Math element ergodic theorem exists finite dimensional function defined Hausdorff space Hence Hilbert space homeomorphism ibid inequality integral Lebesgue Lebesgue measure Lemma linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc Proof properties proved real numbers reflexive Riesz Russian Sbornik N. S. scalar self-adjoint semi-group sequentially compact Show simple functions spectral Studia Math subset subspace Suppose theory topological space Trans uniformly Univ valued function Vber vector space weak topology weakly compact zero