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Which of the following is false ?

  1. Any continuous function from $\left [ 0,1 \right ]$ to  $\left [ 0,1 \right ]$ has a fixed point
  2. Any homeomorphism from  $\left [ 0,1 \right )$ to  $\left [ 0,1 \right )$ has a fixed point
  3. Any bounded continuous function from  $\left [ 0,\infty \right )$ to  $\left [ 0,\infty \right )$ has a fixed point
  4. Any continuous function from  $\left ( 0,1 \right )$  to $\left ( 0,1 \right )$  has a fixed point.
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