## An Introduction to Algebraic TopologyThis self-contained treatment of algebraic topology assumes only some knowledge of real numbers and real analysis. The first three chapters focus on the basics of point-set topology, offering background to students approaching the subject with no previous knowledge. Readers already familiar with point-set topology can proceed directly to Chapter 4, which examines the fundamental group as well as homology groups and continuous mapping, barycentric subdivision and excision, the homology sequence, and simplicial complexes. Exercises form an integral part of the text; they include theorems that are as valuable as some of those whose proofs are given in full. Author Andrew H. Wallace, Professor Emeritus at the University of Pennsylvania, concludes the text with a guide to further reading. |

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algebraic arcwise connected barycentric coordinates barycentric subdivision base-point belonging boundary called chain on F Chapter circular disc closed path condition continuous mapping deﬁned deﬁnition deformation denoted dimension element Euclidean simplex Euclidean space example Exercise f and g ﬁnite number ﬁrst place ﬁxed functions geometrical given Hausdorff Hausdorff space homologous modulo homologous to zero homology groups homomorphism homotopic with respect homotopy identity mapping inclusion mapping inﬁnite cyclic integers interval isomorphism joining kernel Let f limit point line segment linear combination linear mapping mapping f modulo F neighbourhood obtained open sets operation oriented simplex p-chain p-simplex pair paths based Pnoor proof Prove quotient group real numbers relative cycle relative homology class represented result satisﬁes sequence set of points shown simplicial complex simply singular simplex speciﬁed sphere subgroup subset subspace suﬂicient surface tetrahedron topological property topological space torus triangle union vertices X X I xoxl yoyl