Talk:Projection from Product Topology is Open

I don't understand. What further justification is needed? The product topology is defined such that if $U_1$ and $U_2$ are open in each of $T_1$ and $T_2$, then $U_1 \times U_2$ is open in $T_1 \times T_2$ by definition. Therefore if $U = U_1 \times U_2$ is open then the first projection of $U$ is open. Okay, so I lost the unnecessary and confusing "$= U_1$" in the statement, but what else am I missing? I need help here. --prime mover (talk) 15:26, 7 October 2012 (UTC)