Suppose F:C→R,C the Cantor set, has bounded total variation. Is there a homeo g:[0,1]→[0,1] and a diffeo (Lipschitz, maybe) f:[0,1]→R such that F=f∘g|C.
PermalinkSubmitted by bonatti on Sat, 06/17/2017 - 16:15
Maybe the homeomorphism g is not required to be defined on [0,1] but only on C. Otherwize, f∘g is necessarily monotonous, and the answer of the question would be trivially "no". Even with that the question still looks strange: someone is able to state hypotheses making the question pertinent?
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Maybe the homeomorphism g is
Maybe the homeomorphism g is not required to be defined on [0,1] but only on C. Otherwize, f∘g is necessarily monotonous, and the answer of the question would be trivially "no". Even with that the question still looks strange: someone is able to state hypotheses making the question pertinent?
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