Onto continuous function

Asked May 23 '21 at 19:13

Active May 23 '21 at 19:20

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Is there exist a onto continuous function from (0,1) to (0,1]

Answer: Yes.

My Attempt:

Let $f: (0,1) \to (0,1]$ such that $f(x) = x$. This is onto itself but I know that if f is onto then Range $(f) =$ Codomain $(f)$. But in this case, It is not possible.

I'm unable to find such type of function. Please help me.

edited May 23 '21 at 19:20

Jyerki menon

asked May 23 '21 at 19:13

Bhai

think about a quadratic which attains a maximum value of $1$ at $x=1/2$ and has zeros at $x=0,x=1$ – C Squared May 23 '21 at 19:18
https://math.stackexchange.com/questions/42308/continuous-bijection-from-0-1-to-0-1/42310#42310 – Evangelopoulos Foivos May 23 '21 at 19:20
Codomain is semi closed interval. But codomain is closed in the link. – Bhai May 23 '21 at 19:27

Onto continuous function

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