{c}

A subset $\Omega\subseteq\mathbb R^n$ is an <open set> if every $x\in\Omega$ admits a radius $r>0$ such that the <open ball>
$$
B(x,r)=\{y\in\mathbb R^n:|y-x|<r\}
$$
is contained in $\Omega$. A subset $F\subseteq\mathbb R^n$ is a <closed set> if its <complement> $\mathbb R^n\setminus F$ is an <open set>. Equivalently, $F$ contains the <limit> of every <convergent sequence> of its points.

Solution

Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2012 / 4 / a / Solution

 Solution (source code)