Take an <irrational number> $a\in(0,1)$. The <density of the rational numbers> provides a <sequence> in $\mathbb Q\cap[0,1]$ converging to $a$, which is outside that <subset>. Thus the <subset> is not <closed> in $\mathbb R$. By the <Heine-Borel theorem>, \b[it is not <compact>], despite being <bounded>.

Solution

Past exam of the metric spaces and complex analysis course of the University of Oxford / 2015 / 1 / c / ii / Solution

 Solution (source code)