## Algebraic topology--homotopy and homology |

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### Contents

Some Facts from General Topology | 1 |

Categories Functors and Natural Transformations | 6 |

Homotopy Sets and Groups | 11 |

Copyright | |

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### Common terms and phrases

abelian group Adams spectral sequence base point BO(n called cell chain complex chain homotopy Chapter clearly cobordism coefficient cofibre cofibre sequence cofinal cofunctor cohomology commutative diagram composite construct Corollary CW-complex Definition deformation retract denote dirlim dual element epimorphism epimorphism for q equivalence classes exact sequence example fibration fibre bundle finite functor given hence homology theory homotopy classes homotopy groups homotopy inverse Hopf Hurewicz homomorphism inclusion isomorphism for q Lemma lim1 manifolds microbundle module monomials monomorphism morphism n-connected natural equivalence natural transformation pointed space polynomial principal G-bundle projection Proof Proposition prove Remark ring spectrum S-duality map satisfies the wedge set of transition Similarly strong deformation retract structure subcomplex subgroup subspace Suppose surjective Theorem Thorn class topological spaces transition functions trivial unique vector bundle weak homotopy equivalence wedge axiom