How to prove that the walrasian demand function $x(p,w)$ is continuous in $p$ and $w$?

If the utility function $$u$$ is continuous and satisfies local nonsatiation, and walrasian demand function $$x(p, w)$$ is a function (i.e. always map to only single values), how to prove that $$x(p,w)$$ is continuous in $$p$$ (price vector) and $$w$$ (wealth)?

• What are $x(p,w)$ and $w(p,w)$? Are they both the same walrasian demand function? – GabMac Oct 19 '19 at 23:35
• Sorry, this was a typo. – Aqqqq Oct 20 '19 at 5:14
• Look at the Theorem of the maximum: en.wikipedia.org/wiki/Maximum_theorem – user24622 Oct 20 '19 at 15:49