let $X$ be a topological space. let $D=\{(x_1,x_2,x_3)\,|\, x_1=x_2\}\subset X^3$ suppose that $\pi_1(X)$ is generated by $g_i, i\in I$ what are the generators of $\pi_1(D)$?
I read that they are elements of the form $(g_i,g_i,1)$ and $(1,1,g_i)$ why?