Which of the following is false ?
- Any continuous function from $\left [ 0,1 \right ]$ to $\left [ 0,1 \right ]$ has a fixed point
- Any homeomorphism from $\left [ 0,1 \right )$ to $\left [ 0,1 \right )$ has a fixed point
- Any bounded continuous function from $\left [ 0,\infty \right )$ to $\left [ 0,\infty \right )$ has a fixed point
- Any continuous function from $\left ( 0,1 \right )$ to $\left ( 0,1 \right )$ has a fixed point.