# Math Help - metric problem

1. ## metric problem

1. Choose a 'minimizing sequence' $d(x_n,y)\rightarrow \inf_{x\in A} d(x,y)$ and use the fact that $A$ is closed.
2. Let there be two such points, $x$ and $z$. Show that any point $w$ on the line segment to join them satisfies $d(w,y)<\inf_{x\in A} d(x,y).$.