Let \(M\) be a metric space . A subset \(B\subseteq M\) is called bounded if there is a number \(r>0\) such that \(d(x,y)\le r\) for all \(x,y\in M\).
Remark
- A set is bounded if its diameter is bounded.
Let \(M\) be a metric space . A subset \(B\subseteq M\) is called bounded if there is a number \(r>0\) such that \(d(x,y)\le r\) for all \(x,y\in M\).