5
$\begingroup$

I am posting this problem in order to break the problem in my previous post Field Extension problem beyond $\mathbb C$.

Notation: $M(\mathbb C):=$ Field of all meromorphic functions on $\mathbb C$, $K:=$ a proper subfield between $\mathbb C$ and $M(\mathbb C)$

Question 1: Let $\sigma\in Aut(K)$ and $c$ is a constant function. Is it true $\sigma(c)$ is again a constant function ?

I will post subsequent questions after getting a good answer (either by myself or someone else). Let us try how far we can go!

  • 0
    If $f_n$ converges fo $f$, what about $\sigma(f_n)$?2012-05-21
  • 2
    @Blah: I don't follow. $\sigma$ is not required to be continuous.2012-05-21
  • 0
    true, otherwise the question would make no sense! my mistake.2012-05-21

1 Answers 1