This is a question from an undegraduate Topology course
Compute the Euler characteristic $\chi(S^2 \times S^3)$
For topological polyhedra $\chi(X \times Y)=\chi(X) \times \chi(Y) \implies \chi(S^2 \times S^3)=\chi(S^2) \times \chi(S^3)$
Need to find $\chi(S^2)$ and $\chi(S^3)$ but I only know how to calculate the Euler characteristic for polyhedra