Hatcher-Algebraic-Topology · Problem 4.G.1

Homotopy Theory

Mathematics — Graph Theory · gluing-constructions

Problem

Show that for a sequence of maps X0→f1X1→f2⋯X_0 \xrightarrow{f_1} X_1 \xrightarrow{f_2} \cdots, the infinite iterated mapping cylinder M(f1,f2,⋯ )M(f_1, f_2, \cdots), which is the union of the finite iterated mapping cylinders M(f1,⋯ ,fn)M(f_1, \cdots, f_n), deformation retracts onto the mapping telescope.

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