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## O

Example: Suppose X is formed from a space Aby attaching ann-cellDn toA along its boundary; that is, X is the union ofA andDn with each point in Sn−1, the boundary of Dn, identified with some point in A by a map δ. Let f : A −→ Y be a map; it will extend to a map X −→ Y exactly when the class given by f ◦ δ is zero in the cohomology group Hn(X,A;πn−1(Y )). In particular, a map from a sphere Sn−1 can be extended to a map from the disk Dn exactly when its class in Hn(Dn, Sn−1;πn−1(Y )) = Hn(Sn;πn−1(Y )) is the zero class.