This is on page 236 from Algebraic Topology by Hatcher, but I don't see where this map is defined before this statement.
How is the map $H_n(M;R) \to H_n(M \mid x; R)$ defined?
2026-04-08 21:05:30.1775682330
How is the map $H_n(M;R) \to H_n(M \mid x; R)$ defined in Hatcher's book AT?
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Homology of pairs is covariant. In particular, the map of pairs $(M, \varnothing) \to (M, M-\{x\})$ (which is just the identity) induces a map $$H_n(M;R) = H_n(M,\varnothing;R) \to H_n(M, M-\{x\};R) = H_n(M\mid x;R).$$ This is the map in question.