how does one explain the following:
"The sphere can be covered by 2 open sets using stereographic projection in such a way that the intersection of these 2 sets is a connected set $W$.Let $p \in W$, if the jacobian of transitions maps is negative then intechange the parameters, so the jacobian will be positive.Since $W$ is connected, the jacobian is positive for every $p \in W$"
thanks.