## Algebraic Local Invariants of Topological SpacesMathematics Division, Air Force Office of Scientific Research, 1958 - Algebraic topology - 144 pages |

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### Contents

10 Local classification theorems | 30 |

12 Pathwise connectedness around a point | 34 |

13 Local homotopy groups | 42 |

5 other sections not shown

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### Common terms and phrases

admissible extension admissible homotopy admissible map basic path coefficient group cohomology compact-open topology completely regular completes the proof complex numbers conic neighborhood conic point connected around xQ continuous real function Corollary countable basis define a homotopy Define a path Define an admissible deformation retract deg g denote the natural denote the subspace element exists a homotopy exists a path exists an open f and g f induces following property following Theorem given local map given triplet grotp Hausdorff space homo topic homology theory homotopy classes homotopy groups Hopf theorem identity map immediate consequence inclusion map ind f induced homomorphisms integer isomorphisms Let f local homotopy groups locally homotopic map f map of X,x maps f,g n-connected natural projection neighborhood of xQ open neighborhood pathwise accessible pathwise connected point xQ positive real number singular homology sub space tangent space topological space X,xQ