Algebraic Topology: An Introductory Course, 1967-1968Courant Institute of Mathematical Sciences, New York University, 1969 - Algebraic topology - 321 pages |
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abelian group acyclic algebraic argument assertion axiom base point called canonical neighborhood chain chain-complexes chain-homotopy closed simplex coefficients cohomology commutative compact connected consider Corollary covering map covering space D₁ define definition denote diagram differential groups dimension edge path element equivalence relation exact couple example exists Ext A,B fact fiber-map filtration finite finitely-generated follows free abelian free abelian group function functor fundamental group G₂ given graded H-space h₁ H₂ Hilton-Wylie Hom A,B homology groups homology theory homomorphism homotopy class induced integer isomorphism K₁ K₂ Künneth formula lemma map f morphism natural chain-maps Observe obtained open sets path-connected Plainly polyhedra polyhedron Proof Proposition reader Rees system Remark short exact sequence simplex simplicial approximation simplicial complex simplicial map singular singular homology singular theory spectral sequence subcomplex subdivision subgroup subset Suppose topological space unique vertex vertices X,xo x₁ хо