Topological equivalence of discontinuous norms

We show that for every p > 0 there is an autohomeomorphism h of the countable infinite product of lines R-N such that for every r > 0, h maps the Hilbert cube [-r,r](N) precisely onto the "elliptic cube" {x is an element of R-N : Sigma(i=1)(infinity)\x(i)\(p) less than or equal to r(p)}. This means that the supremum norm and, for instance, the Hilbert norm (p = 2) are topologically indistinguishable as functions on R-N. The result is obtained by means of the Bing Shrinking Criterion.