## Linear Operators: General theory |

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Page 18

A continuous one - to - one map from a compact space to a

homeomorphism . PROOF . Let X be a compact space , Y a

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

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

Page 274

Let S be a compact

continuous functions on S . Let A be a closed subalgebra of C ( S ) which

contains the unit e and contains , with f , its complex conjugate f defined by f ( s )

= f ( s ) .

Let S be a compact

**Hausdorff space**and C ( S ) be the algebra of all complexcontinuous functions on S . Let A be a closed subalgebra of C ( S ) which

contains the unit e and contains , with f , its complex conjugate f defined by f ( s )

= f ( s ) .

Page 276

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

distinguish between the points of S . Then there exists a compact

each f ...

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

distinguish between the points of S . Then there exists a compact

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

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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