Hahn-Banach distance formula
= Hahn-Banach distance formula
{c}
For a closed subspace $Y$ of a normed space $X$,
$$
d(x,Y)=\sup\{|f(x)|:f\in X^*,\ \lVert f\rVert\leq1,\ f|_Y=0\}.
$$
This is the dual norm formula in the quotient $X/Y$.
= Hahn-Banach distance formula
{c}
For a closed subspace $Y$ of a normed space $X$,
$$
d(x,Y)=\sup\{|f(x)|:f\in X^*,\ \lVert f\rVert\leq1,\ f|_Y=0\}.
$$
This is the dual norm formula in the quotient $X/Y$.