A subset $A$ is <connected space>[connected] if its <subspace topology> admits no separation into two disjoint nonempty relatively open subsets. Equivalently, every <continuous map> $A\to\{0,1\}$, with the target discrete, is constant: a nonconstant map gives the separation by its two fibers, and a separation defines such a map.

Solution

Past exam of the options II course of the University of Oxford / 2010 / E / E3 / a / i / Solution

 Solution (source code)