## An introduction to abstract analysis |

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### Contents

Basic ideas l | 1 |

Some simple results ll | 11 |

Open and closed sets | 30 |

Copyright | |

12 other sections not shown

### Common terms and phrases

analysis argument bijection bounded set Br(a Calculate Cauchy sequence chapter choose closed sets closed subset compact set compact subset concept consider contains continuous function continuous mapping converges uniformly Corollary countable set cr(E deduce defined by f(s,t definition denote dense Df(x distance element example exercises exists fact Firstly fixed point fn(s follows Fourier series function g g is continuous given gradient vector Hence idea inequality infimum integral interior point interval inverse Lemma Let f Let g limit linear mapping means non-empty normed linear space notation obtain open ball open covering open set partial derivatives point of closure pointwise polynomial Proof prove real numbers real-valued function relative minimum result Riemann Riemann-integrable scalar sequence xn Show simple Suppose f supremum theorem theory totally bounded totally bounded set uniformly continuous uniformly convergent unique univariate write zero