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$(a)$ Is it possible to partition the segment $[0,1]$ into t

Source: Eatonia IMO TST 1997 Day 2 P1

November 27, 2015
intervalSets

Problem Statement

(a)(a) Is it possible to partition the segment [0,1][0,1] into two sets AA and BB and to define a continuous function ff such that for every x∈A f(x)x\in A \ f(x) is in BB, and for every x∈B f(x)x\in B \ f(x) is in AA?
(b)(b) The same question with [0,1][0,1] replaced by [0,1).[0,1).
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