Topological equivalence of discontinuous norms

J.J. Dijkstra, J. van Mill

Research output: Contribution to JournalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)177-196
JournalIsrael Journal of Mathematics
Publication statusPublished - 2002


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