## Topology |

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### Contents

CHAPTER | 1 |

Topology of the Line R | 2 |

Limit of a Sequence The Cauchy Criterion for Convergence | 6 |

Copyright | |

44 other sections not shown

### Common terms and phrases

absolutely summable accumulation point arbitrary ball with center bounded Cauchy criterion Cauchy sequence class with ratio closed sets compact metric space compact set compact space contains continuous functions continuous mapping convex function Corollary countable Deduce Definition denote ecart equivalent to saying everywhere dense example family of elements filter base finite number follows hence Hilbert space homeomorphism identical implies inequality infinite product integer intersection isomorphism Lemma limit linear functional linear mapping Lipschitz class locally compact lower semicontinuous multipliable neighborhood base nonempty normed space open ball open interval open set orthogonal orthonormal pointwise polynomials prehilbert space Proof properties Proposition real numbers relation satisfies the Cauchy scalar product seminorm separated space sequence of points sequence xn set of points Show space F summable families supremum Theorem topological group topological space topology associated uniform convergence uniformly continuous vector subspace