Which of the following statements are true about the open interval (0,1) and the closed interval [0,1]?
I. There is a continuous function from (0,1) onto [0,1].
II. There is a continuous function from [0,1] onto (0,1).
III. There is a continuous one-to-one function from (0,1) onto [0,1].
III is definitely wrong. Because if there is one-to-one function, the topological property of the domain and range should be same.
I is true. There is an example on sfmathgre.blogspot.com
But any thoughts on why II is wrong?