Titlebook: An Introduction to Algebraic Topology; Joseph J. Rotman Textbook 1988 Springer-Verlag New York Inc. 1988 Algebraic topology.CW complex.Fun

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Introduction,out topological spaces and continuous functions into problems about algebraic objects (e.g., groups, rings, vector spaces) and their homomorphisms; the method may succeed when the algebraic problem is easier than the original one. Before giving the appropriate setting, we illustrate how the method w

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Singular Homology,hether a union of .-simplexes in a space . that “ought” to be the boundary of some union of (. + 1)-simplexes in X actually is such a boundary. Consider the case . = 0; a 0-simplex in . is a point. Given two points x., x. ∈ ., they “ought” to be the endpoints of a 1-simplex; that is, there ought to

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Simplicial Complexes,few cases in which we could compute these groups. At this point, however, we would have difficulty computing the homology groups of a space as simple as the torus . = . x .; indeed .(.) is uncountable for every . ≥ 0, so it is conceivable that .(.) is uncountable for every . (we shall soon see that

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Homotopy Groups,s from S. into .. It is thus quite natural to consider (pointed) maps of . into a space .; their homotopy classes will be elements of the . .(., x.). This chapter gives the basic properties of the homotopy groups; in particular, it will be seen that they satisfy every Eilenberg-Steenrod axiom save e

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