## Banach spaces of continuous functions, Volume 1 |

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### Contents

Basic notation | 15 |

ELEMENTS OF SET THEORY | 25 |

ORDERED AND TOPOLOGICAL SPACES | 32 |

Copyright | |

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### Common terms and phrases

assume Baire Banach spaces bijection bocof Boolean algebra Borel bounded linear operator cardinal number closed subset commutative Comp compactification conditions are equivalent Consequently continuous functions continuous map continuous surjection convergent convex set coproduct Corollary corresponding countable covariant functor decomposition defined Definitions dense diagram disjoint dyadic elements Exercises exists a unique finite following conditions Hausdorff space hence Hint homeomorphic ideal iff there exists implies infimum inverse isomorphic Lemma Let F locally compact space Math metric space Moreover morphism natural equivalence natural transformation nonempty normed vector space notion object one-to-one open sets open-closed ordered space ordinal preordered Proc projection Proof Proposition proved quotient map representation reticulated retraction satisfying the following scalar Semadeni sequence space and let subalgebra submorphism subspace Suppose supremum surjection tensor product theorem theory topological space uniformizable vector lattice weak topology weakly