Let http://data.artofproblemsolving.com/...b9db40e747.gif be a continuously differentiable function between two open sets in http://data.artofproblemsolving.com/...19f70b47b1.gif. Suppose

that the Jacobian determinant of f is never zero on http://data.artofproblemsolving.com/...e0c0389dd6.gif, that http://data.artofproblemsolving.com/...da6040d22c.gif is compact for any compact subset

http://data.artofproblemsolving.com/...dcf2b9f569.gif of http://data.artofproblemsolving.com/...46259e187b.gif, and that http://data.artofproblemsolving.com/...46259e187b.gif is connected. Show that http://data.artofproblemsolving.com/...04ac4367a4.gif .