## Rings of continuous functions |

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A favorite in the library of topologists and analysts. The book starts with the title, i.e. none of the concepts in the title are defined, so if you don't understand those terms don't start with this book. Given that the reader is fairly familiar with the terms in title the book is a fairly pleasant read. Focuses mostly on spaces which are Tychonoff/completely regular. (Those continuous functions are into the reals.)

### Contents

chapter page 0 Foreword | 1 |

Functions on a Topological Space | 10 |

Ideals and zFilters | 24 |

Copyright | |

18 other sections not shown

### Common terms and phrases

algebraic analytic subring arbitrary belongs C-embedded cardinal Cauchy z-filter Chapter closed sets closure cluster point cofinal compact set compact space compactification completely regular space completely separated contains a copy continuous extension continuous functions continuous mapping converges Corollary countably compact Dedekind-complete defined denote dense discrete space disjoint closed sets element equivalent exists extremally disconnected finite intersection property follows free ideal free maximal ideal given Hausdorff space Hence homomorphism hyper-real hypothesis ideal in C(X implies induced infinitely large isomorphism Lemma locally compact lower ideal maximal ideal metric space neighborhood nonempty nonmeasurable one-one open sets open-and-closed sets ordered field P-point P-space prime ideals contained proof pseudocompact pseudocompact space pseudometric real number real-closed realcompact space result ring subring subset subspace Theorem totally ordered ultrafilter uniform space uniform structure unique upper ideal weak topology z-ideal zero-set