What are the isometries of the Hilbert Cube I^\infty = the set of all sequences (x_i) such that x_i \in [0, 1] endowed with the metric
d((x_i), (y_i)) = \sum_{i=0}^\infty 2^{-i} |x_i - y_i| ?
Konrad Burnik
My conjecture is that the only possible isometries of the Hilbert Cube (in this metric) are
f(x_i) = (y_i) such that y_i = x_i or y_i = 1 - x_i
where (x_i) and (y_i) denote sequences in I^\infty and x_i, y_i denote their i-th terms, respectively.
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Waldemar Barrera
Do you know good references on the subject? I seems a question very innocent but it is very hard!
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