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Quotient maps

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New member
Oct 15, 2013
19
Hello everyone

The problem which I am stuck on is:
show that there is a quotient map $(0,1)\rightarrow[0,1]$, but not $[0,1]\rightarrow(0,1)$

For the second part, I think I solved it, the reason is $[0,1]$ is compact while $(0,1)$ is not.
However, for the first part, I think I need to find a continuous onto map between them, but I have no idea about that map, how to cover point $0$ and point $1$.
Hope someone can help me out.
Thanks