spherically complete

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spherically complete

Needed to prove Hahn-Banach for ultrametric spaces: attachments/Pasted%20image%2020220605232436.png

Consequences:

  • Every shrinking map (not just contracting maps) has a unique fixed point.
  • If \(Y\hookrightarrow X\) with \(Y\) spherically complete then for every \(x\in X\) there exists a (non-unique) best approximation in \(Y\).
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