A map, maps each point of the middl third Cantor set C, considered as a subset of real numbers between 0 an 1 written in base 3 and containing only digits 0 and 2, to the set of real numbers I = [0, 1] written in base 2, where bi = ai/2. Prove

a) the map is continuous of C onto I

b) prove the map is not bijective

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2. Consider a map (,0 : C > I, which maps each point of the middle third Cantor set C, considered as a subset of real numbers between 0 and 1 written in base 3 and containing only digits 0 and 2, to the set of real numbers I = [0,1] written in base 2, according to the rule 0.046520% > 0.b1b2b3 . . ., where b,- = %. (a) Prove that (,0 is a continuous map of C onto I. (b) Prove that (,0 is not bijective