## TopologyDesigned as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity. |

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#### LibraryThing Review

User Review - johnnylogic - LibraryThingDelightful text emphasizing point-set and the significance of limit sets. Much more readable than the elegant, yet rarified Kolmolgorov. Read full review

### Contents

TOPOLOGICAL SPACES AND FUNCTIONS | 1 |

THE ELEMENTS OF POINTSET TOPOLOGY | 37 |

FURTHER TOPICS IN POINTSET TOPOLOGY | 105 |

Copyright | |

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### Common terms and phrases

1-cycle 1-simplexes abelian algebraic Axiom barycentric subdivision basis elements boundary Cantor set Cech cycle Cech homology chain group chain-mapping closed sets closed subset closure cochain coefficients cohomology collection compact Hausdorff space compact space component consider continuous mapping continuum coordinates COROLLARY defined definition denote dimension equivalent Euclidean example EXERCISE finite number follows free group function geometric given group Cp(K Hausdorff space hence homeomorphism homology groups homology theory homotopy Hp(K induced homomorphisms infinite integer intersection interval inverse limit isomorphic LEMMA lies limit point locally compact locally connected n-cell n-sphere nonempty open set open set containing p-chain pair Peano space polytope Proof prove reader real numbers result satisfies Section separable sequence simple chain simplex simplicial complex simplicial mapping Sn~l subcomplex subgroup subspace Suppose Theorem topological group topological space topology torus triangulation union vector vertex vertices zero