<Convergence of a sequence in a topological space>[Convergence of a sequence] to $\ell$ means that every <open neighbourhood> $U$ of $\ell$ contains all sufficiently late terms: there is $N$ such that $x_n\in U$ for all $n\geq N$. The threshold may depend on $U$.

Solution

Past exam of the options I course of the University of Oxford / 2009 / E / E1 / a / iii / Solution

 Solution (source code)