Hatcher-Algebraic-Topology · Problem 4.1.23

Homotopy Theory

Mathematics — Graph Theory · mapping-cone-cw-type

Problem

f : X \to Y

is a map with

X

and

Y

homotopy equivalent to CW complexes, show that the pair

(M_f, X)

is homotopy equivalent to a CW pair, where

M_f

is the mapping cylinder. Deduce that the mapping cone

C_f

has the homotopy type of a CW complex.