Norm from a bounded symmetric convex neighbourhood
= Norm from a bounded symmetric convex neighbourhood
{title2=$p_U(x)=\inf\{t>0:x\in tU\}$}
For a bounded convex open set $U$ containing zero and invariant under $x\mapsto-x$, its <Minkowski functional> is a <norm>. Inner and outer Euclidean balls give positive finite bounds; symmetry and scaling give absolute homogeneity; convexity gives the <triangle inequality>. Openness makes $U=\{p_U<1\}$, while boundedness prevents nonzero vectors from having zero gauge.