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Exercises

  1. [0SB]Prerequisites:[0QR]. Show that the set \(A⊂ ℝ\) defined by

    \[ A=\{ 0\} ∪ \{ 1/n : n∈ℕ, n≥ 1\} ∪ \{ 1/n+1/m : n,m∈ℕ, n≥ 1, m≥ 1\} \]

    is compact; identify its accumulation points.

    Solution 1

    [0SC]

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  • accumulation point, in metric spaces
  • metric space
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