Why are there no continuous one-to-one functions from (0, 1) onto [0, 1]? – math.stackexchange.com

Why are there no continuous one-to-one functions from (0, 1) onto [0, 1]? – math.stackexchange.com

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I do not understand the justification of why III is false, could anyone clarify this for me please? Question 65. Which of the following statements are true about the open interval $(0,1)$ and the ...

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