\b[True.] Coordinate projections define $\pi_1(X\times Y,(x,y))\to\pi_1(X,x)\times\pi_1(Y,y)$. A pair of based loops gives the inverse by $t\mapsto(\gamma_X(t),\gamma_Y(t))$. Homotopies combine and project coordinatewise, and loop concatenation does too. These maps are well-defined inverse group homomorphisms, requiring no local connectedness assumptions.


Solution

Past exam of the mathematics course of the University of Cambridge / 2011 / ii / Paper 1 / 21H / iii / Solution

 Solution (source code)