Consider the field ℂ together with the Euclidean topology. Let K be a proper subfield of ℂ that is not contained in ℝ. Which one of the following statements is necessarily true?
1
K is dense in ℂ.
2
K is an algebraic extension of ℚ.
3
ℂ is an algebraic extension of K.
4
The smallest closed subset of ℂ containing K is NOT a field.