Mathematics Tripos Papers

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  • Part IB
  • Part II
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Paper 3, Section I, 3E3 \mathrm{E}3E

Metric and Topological Spaces | Part IB, 2015

Define what it means for a topological space XXX to be (i) connected (ii) path-connected.

Prove that any path-connected space XXX is connected. [You may assume the interval [0,1][0,1][0,1] is connected. ]]]

Give a counterexample (without justification) to the converse statement.

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