Hatcher 0.24

Hatcher, Algebraic Topology, Chapter 0

24. Let X and Y be CW complexes with 0-cells x_0 and y_0. Show that the quotient spaces X*Y/(X*\{y_0\}\cup\{x_0\}*Y) and S(X\wedge Y)/S(\{x_0\}\wedge\{y_0\}) are homeomorphic, and deduce that X*Y\simeq S(X\wedge Y).

Proof.

   \square

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