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Notations and Prerequisites
Connected and Disconnected Spaces
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Algebraic Topology bijective chapter choose closed subsets commutative compact subset complex numbers connected constant map construction contains continuous map corollary to Theorem deduce definition denote diagram differentiable direct sum disjoint disk duality theorem element equivalence classes equivalence relation euclidean space exact sequence example EXERCISES AND PROBLEMS exists extends finite set follows free abelian group function give given graph hence Hl(X Hl(Y homogeneous coordinates homomorphism homotopy classes homotopy equivalent Horn identity map implies induces injective integer intersection interval inverse isomorphism joining Jordan curve theorem Lemma Let loop map f neighborhood nonempty notation nullhomotopic obtain open sets open subsets path components path-connected plane points preceding exercise proof of Theorem prove real numbers result Show Similarly Spanier straight line segments subgroup subspace suppose surjective Theorem 9.4 Theorem Let union universal property vertices write zero