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An introduction to algebraic topology Joseph J. Rotman
Publisher: Springer

Julia Collins, Homological algebra (2006) (pdf). 3 Topological Vector Spaces Schaefer, Wolff. Topology: Bott and Tu's Differential Forms in Algebraic Topology is a very readable introduction to smooth manifolds and goes far; everyone should read it. Another book that's slightly less advanced, but introduces some of the more basic aspects of homotopy theory, is Brayton Gray's Homotopy Theory: An Introduction to Algebraic Topology. 1 Introduction to Axiomatic Set Theory Takeuti, Zaring. Rick Jardine, Homological algebra These are both absolutely crucial ingredients in the modern theory of homological algebra, yet for the next twenty years homology theory was to remain confined to the realm of topology. 4 A Course in Homological Algebra Hilton, Stammbach. This treats algebraic topology using tools of strict ω-groupoid-theory: notably the traditional homological algebra use of chain complexes of abelian groups is generalized to crossed complexes, and emphasis is put on the notion of fundamental groupoid and its strict higher categorical generalizations to the cubical fundamental So I decided to use this account for the book, thus giving students the advantage, it seemed, of an introduction to cohomological ideas. Introduction to Topology 1: Open and Closed Sets · Introduction to Topology 3: Limit Points, Boundary Points, and Sequential Limits → The idea is pretty much similar to basis of a vector space in linear algebra. Alexander Beilinson, Introduction to homological algebra (handwritten notes, summer 2007, pdf) lec1, lec2, lec3, lec4. Download Homology theory: A first course in algebraic topology (Holden-Day series in mathematics) Homology Theory: A First Course in Algebraic. Amazon.com: Customer Reviews: Homology Theory: Introduction to. Topics covered in the seminars in analysis 18.104), logic (18.504), and algebra (18.704), vary from year to year. Number theory: Serre, A Course in Arithmetic.