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Show that the closure of S is closed.Solution .pdf

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Show that the closure of S is closed. Solution Let T be the complement of the closure. For any point t in T, thereis a ball around t that does not intersect S. (Else t would be inthe closure, not its complement.) Hence the ball is in T. We just showed T is open. Hence its complement is closed..

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Show that the closure of S is closed. Solution Let T be the complement of the closure. For any point t in T, thereis a ball around t that does not intersect S. (Else t would be inthe closure, not its complement.) Hence the ball is in T. We just showed T is open. Hence its complement is closed.

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Show that the closure of S is closed.Solution .pdf

  • 1. Show that the closure of S is closed. Solution Let T be the complement of the closure. For any point t in T, thereis a ball around t that does not intersect S. (Else t would be inthe closure, not its complement.) Hence the ball is in T. We just showed T is open. Hence its complement is closed.