EDB — 0Q8

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E29

[0Q8] Prerequisites:[0PD],[0PP], [0GJ], [0P6].Difficulty:*.

Let X be a metric space, and AX. We want to study the ”open-close” operation (A) (which is the closure of the interior of A).

  • Show a simple example where (A) is not contained A.

  • Then write a characterization of (A) using sequences and balls.

  • Use it to show that the ”open-close” operation is idempotent, that is, if D=(A) and then E=(D) then E=D.

Solution 1

[0Q9]

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Bibliography
Book index
  • accumulation point, in metric spaces
  • topology, in metric spaces
  • metric space
  • closure
  • interior
  • open-close
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