 Solution

ID: past-exam-of-the-metric-spaces-and-complex-analysis-course-of-the-university-of-oxford/2015/2/a/i/solution

A metric space is connected when it has no separation of a topological space: it cannot be written as the union of two disjoint nonempty open subsets. Equivalently, the only subsets that are both open and closed are the empty set and the whole space.

X connected ⟺ no two disjoint nonempty open sets cover X .

The open sets here are those of the metric topology.

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