Entire functions mapping countable dense subsets of the reals onto each other monotonically

Daihachiro Sato, Stuart Rankin
1974 Bulletin of the Australian Mathematical Society  
It is shown that for arbitrary countable dense subsets A and B of the real line, there exists a transcendental entire function whose restriction to the real line is a real-valued strictly monotone increasing surjection taking A onto B . The technique used is a modification of the procedure Maurer used to show that for countable dense subsets A and B of the plane, there exists a transcendental entire function whose restriction to ^ is a bijection from A to B .
doi:10.1017/s0004972700040636 fatcat:jqh2caftgret3k2cowwp5e5cvq