I have this problem and I don't know how to deal with it... No idea at all... Here it is:
Given an exchange economy of two goods and one consumer, with initial good $\displaystyle \omega=(4,3)$. Show that the multi-valued function
$\displaystyle \varphi{(p)}=B_{\omega}(p)=\left \{x \in \mathbb{R}_{+}^{2} | p \cdot x \leq p \cdot \omega \right \}, p>>0$
is continuous.