EDB — 0PQ

Exercises

1. [0PQ] Topics:closure.Prerequisites:[0P6]↺↻, [0PN]↺↻.

   Given a metric space \(X\) and a set \(A⊆ X\), show that

   \[ \overline A= \overline{\left(\overline A\right)} \]

   either by transitioning to the complement set and using [0PJ]↺↻, or by using the definition of \(\overline A\) as ”set of adherent points”.

   As discussed in [0PM]↺↻, this is equivalent to saying that \(\overline A\) is a closed set.