{c}

A <path-connected space> $S$ has, for every pair $z_0,z_1\in S$, a <continuous> path $\gamma:[0,1]\to S$ with $\gamma(0)=z_0$ and $\gamma(1)=z_1$. Every <path-connected space> is a <connected space>, because a separation of the target would pull a joining path apart and contradict <connectedness of an interval>.

Solution

Past exam of the algebra, analysis and differential equations 1 course of the University of Oxford / 2011 / 4 / iii / Solution

 Solution (source code)