 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-1-course-of-the-university-of-oxford/2011/4/iii/solution

S

has, for every pair

z_{0}, z_{1} \in S

γ : [0, 1] \to S

with

γ (0) = z_{0}

and

γ (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.

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