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In algebraic topology, the homotopy excision theorem offers a substitute for the absence of excision in homotopy theory. More precisely, let {\displaystyle } be an excisive triad with C = A ∩ B {\displaystyle C=A\cap B} nonempty, and suppose the pair {\displaystyle } is -connected, m ≥ 2 {\displaystyle m\geq 2} , and the pair {\displaystyle } is -connected, n ≥ 1 {\displaystyle n\geq 1}. Then the map induced by the inclusion i : → {\displaystyle i\colon \to } ,
is bijective for q < m + n − 2 {\displaystyle q A geometric proof is given in a book by Tammo tom Dieck. This result should also be seen as a consequence of the most general form of the Blakers–Massey theorem, which deals with the non-simply-connected case.