Notation • X « Y means that the topological spaces X and Y are homeomor- phic • X ~ Y means that the topological spaces X and Y are homotopy equivalent • f ~ g means that the map / is homotopic to g\ • \A\ denotes the cardinality of the set A\ • int A denotes the interior of A • A denotes the closure of A • dA denotes the boundary of A • id^ denotes the identity map on A • Kn denotes the complete graph on n vertices • -^n,7n5 see p. (\ • Dn denotes the n-disk (or n-ball) • Sn denotes the n-sphere • A n denotes the n-simplex • In denotes the n-cube • P2 denotes the projective plane • T2 denotes the two-dimensional torus • S2#nP2 and nP2 denote the connected sum of n projective planes • S2#nT2 and nT2 denote the connected sum of n 2-tori (the sphere with n handles) • K2 denotes the Klein bottle XI

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