A nonconvex set which has the unique nearest point property (Q1099024)

The author constructs a subset S of the real inner product space E of all real sequences having at most a finite number of nonzero terms, with inner product \((x,y)=\sum_{i}x_ iy_ i\), where \(x=(x_ 1,x_ 2,...)\), \(y=(y_ 1,y_ 2,...)\), and induced norm \(\| x\| =\sqrt{(x,x)}\), such that S is closed and nonconvex; S is not a sun; each point in E has an unique nearest point in S and the metric projection for S is continuous.