From Vectorcalcumb

Vector Extreme Value Theorem

<m>F: \\bbR^n \\right \\bbR^M</m>
<m>F</m> is continuous, <m>A \\subset \\bbR^N</m>
<m>\\right</m> F is bounded and obtains miminum and maximum values
i.e. <m> F(A)</m> is compact

And apparently, there's no analogue to the Intermediate Value Theorem in Vector Calculus.

And then I have these scribblings: <m> F(A) \\subset</m>