Construct an explicit bijection from (0,1) to [0,1]

**qtpipi** · April 14th 2009, 06:10 PM

Construct an explicit bijection from the open interval (0,1) to the closed interval [0,1].

**NonCommAlg** · April 14th 2009, 11:26 PM

Originally Posted by qtpipi

Construct an explicit bijection from the open interval (0,1) to the closed interval [0,1].

how about this: $f(x) = \begin{cases} 0 & x = \frac{1}{2} \\ \frac{1}{n-2} & x =\frac{1}{n} , \ n \geq 3, \ n \in \mathbb{N} \\ x & \text{otherwise} \end{cases}.$

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