The closure in a Hilbert space of a preHilbert space Chebyshev set that fails to be a Chebyshev set

In 1987 the author gave an example of a non convex Chebyshev set SS in the incomplete inner product space EE consisting of the vectors in l2l2 which have at most a finite number of non zero terms. In this paper, we show that the closure of SS in the Hilbert space completion l2l2 of EE is not Chebyshev in l2l2.