# 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.

$\square$