## Fundamentals of topology |

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### Contents

Introduction | 1 |

Topological Spaces | 17 |

The Separation Axioms | 45 |

Copyright | |

8 other sections not shown

### Common terms and phrases

arcwise connected axioms Bolzano-Weierstrass property Cauchy filter Cauchy sequence closed subsets collection collectionwise normal compact iff compact subspace compactification completely normal completely regular connected iff converges countably compact define DEFINITION denote dense equivalence relation EXERCISES Figure finite subcover fixed-point property Hausdorff space Hence hereditary homeomorphic homology sequence homology theory homotopically equivalent homotopy identity mapping iff there exists implies infinite cyclic integer intersection isomorphism lattice lemma Let G locally compact locally connected modulo Moreover n e I+ nonempty open cover open sets pair mapping paracompact partially ordered path component pathwise connected Proof Prove Theorem pseudometric quotient reader real numbers retract screenable second countable semimetric sequentially compact Show singular homology singular homology groups subbase suppose T0-space topological property topological space totally bounded uniform space x e G