Does this function exist

Calculus Level 3

Does there exist an injective function f : R R f: \mathbb{R} \rightarrow \mathbb{R} such that every element of the image of f f is an isolated point of the image of f ? f?


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1 solution

Jonathan Dunay
Jan 9, 2018

No. Any set of isolated points is countable. Since the function is injective, this makes the domain countable giving a contradiction.

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