A <topology> on $X$ is a family $\mathcal T$ of subsets containing $\varnothing$ and $X$, closed under arbitrary unions and finite intersections. Its members are the <open sets>. A <Hausdorff space> separates each pair of distinct points by disjoint open neighbourhoods; a <compact space> is one for which every <open cover> has a finite subcover.

Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / ib / Paper 1 / 12F / Solution

 Solution (source code)