3. (1) Consider A = [0, 1] and B = [0, 1) and injections f(x) = x/3 from A to Band g(x) = x from B to A. Construct a bijection h from A to B such that on some points of A, h(x) = f(x), and for the other points of A, h(x) = g-'(x).

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I cannot come up with good bijection! Could you help me with detailed explanation?

3.
(1) Consider A = [0, 1] and B = [0, 1) and injections f(x) = x/3 from A to
Band g(x) = x from B to A. Construct a bijection h from A to B such that on some points
of A, h(x) = f(x), and for the other points of A, h(x) = g-'(x).
Transcribed Image Text:3. (1) Consider A = [0, 1] and B = [0, 1) and injections f(x) = x/3 from A to Band g(x) = x from B to A. Construct a bijection h from A to B such that on some points of A, h(x) = f(x), and for the other points of A, h(x) = g-'(x).
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