## Topology; a First CourseFor a one or two semester introduction to topology at the senior or first year graduate level. |

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### Contents

and Continuous Functions | 75 |

Connectedness and Compactness | 146 |

Countability and Separation Axioms | 189 |

Copyright | |

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algebra assert Baire space basis element belongs bijective box topology called choose closed sets closed subset closure collection compact Hausdorff space compact space compactification completely regular Consider continuous functions continuous map Corollary countable basis covering map covering space define definition denote the set dictionary order disjoint open sets equals equation equicontinuous equivalence classes equivalence relation Example Exercise exists fact function g fundamental group given Hausdorff space Hint homeomorphic homotopy imbedding induced infinite injective intersection interval isomorphism least upper bound locally compact locally finite loop n e Z+ neighborhood normal space one-point sets open covering open sets order relation order topology ordered set paracompact path homotopy plane point x0 positive integers product topology proof properties quotient map rational numbers real line real numbers retract satisfies sequence Show simply connected simply ordered smallest element subspace topology Suppose surjective topological space uncountable union well-ordered set