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> 1. Show $f:\mathbb{R}^2\to\mathbb{R}, f(x\_1,x\_2)=x\_1$ is continuous.
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How should I proceed?

Fix $\epsilon>0 |f(x\_1,x\_2)-f(x\_3,x\_4)|<\epsilon\Rightarrow |x\_1-x\_3|<\epsilon\Rightarrow$ choose $\delta=\epsilon$ 

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> 2. $A$ is open in $\mathbb{R}$, $B=\{(x\_1,x\_2): x\_1\in A\}$, show $B$ is open in $\mathbb{R}^2$.
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If (1) is shown then I can directly tell inverse image of open set is open. thanks for helping