Elements of homotopy theory
The writing bears the marks of authority of a mathematician who was actively involved in setting up the subject. Most of the papers referred to are at least twenty years old but this reflects the time when the ideas were established and one imagines that the situation will be different in the second volume. Because of the length, it is unlikely that many people will read this book from cover to cover, but it will be used for reading up on a particular topic or dipping into for sheer pleasure - and the fact that the details may not be quite as expected should add to the enjoyment.
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Standard Notations and Conventions
Compactly Generated Spaces
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abelian group base point boundary operator cell cellular chain complex chain map Chapter characteristic map cochain cohomology operation commutative diagram compactly composite connected Corollary cross product defined deformation retract dimension direct sum element epimorphism example fact fibration fibre F finite follows functor H-space Hence Hn(X homology groups homology theory homomorphism homotopic rel homotopy class homotopy lifting homotopy sequence homotopy type Hq(X Hr(X Hurewicz map Hurewicz Theorem identification map identity map inclusion map induced injection integer isomor isomorphism isomorphism for q l)-connected Let f Let G map f map g map h monomorphism Moreover morphism n-cell n-connected NDR-pair nn(X nq(X nullhomotopic obstruction one-to-one correspondence oriented pair partial lifting path phism proof properties prove relative CW-complex relative homeomorphism represents respectively singular space subcomplex subgroup subset subspace Suppose suspension Theorem Let topology trivial weak homotopy equivalence Whitehead