Spooky geometry IV

Let [a,b] and [c,d] be subintervals of [0,1] and call them non-overlapping if they intersect only possibly in their endpoints. Construct a continuous curve \sigma:[0,1]\to H with H a Hilbert space, such that if [a,b] and [c,d] are any non-overlapping subintervals of [0,1], then \sigma(b)-\sigma(a) and \sigma(d)-\sigma(c) are orthogonal.

Harder: show that this can be carried out in any infinite-dimensional Hilbert space.

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Spooky geometry IV

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