This swift and concise presentation of the fundamental principles and result of algebraic topology follows the axiomatic foundations pioneered by means of Eilenberg and Steenrod. The strategy of the booklet is pragmatic: whereas such a lot proofs are given, those who are rather lengthy or technical are passed over, and effects are said in a sort that emphasizes useful use over maximal generality. in addition, to raised display the logical constitution of the topic, the separate roles of algebra and topology are illuminated.
Assuming a heritage in point-set topology, Fundamentals of Algebraic Topology covers the canon of a first-year graduate direction in algebraic topology: the elemental staff and protecting areas, homology and cohomology, CW complexes and manifolds, and a brief advent to homotopy concept. Readers wishing to deepen their wisdom of algebraic topology past the basics are guided via a quick yet rigorously annotated bibliography.
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