## Counterexamples in analysis |

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### Contents

The Real Number System | 3 |

Functions and Limits | 20 |

A function continuous and onetoone on an interval | 27 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

absolute value addition and multiplication arbitrary assumed binary operation Cantor function Cantor set Chapter closed interval closed set coefficients compact complex numbers contains continuous functions convergent series countable defined Definition deleted denned denoted dense set derivative disjoint equal everywhere continuous Example 15 Example 23 fn(x follows function continuous function of Example homeomorphic identically integral domain irrational numbers Lebesgue Lebesgue-integrable limit point linear mapping measure zero metric space monotonic function natural numbers neighborhood nonempty set nonmeasurable nonzero one-to-one correspondence open interval open sets ordered field ordered field SF partial sums plane measure points of discontinuity polynomial positive integer positive measure positive number properties rational function rational numbers real number system real variable real-valued function region Riemann Riemann-integrable Riemann-integrable function set of measure set of points set Q simple arc square subintervals subset theorem topological space topology unbounded uniformly continuous upper bound vector