transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
An automorphism of the field of complex numbers.
Beyond the two evident ones, the identity and complex conjugation, there is an infinitute of “wild” automorphisms, which, however, are not continuous and not constructive (their existence requires Zorn's lemma).
H. Kestelman, Automorphisms of the Field of Complex Numbers, Proceedings of the London Mathematical Society, Volume s2-53, Issue 1, 1951 (doi:10.1112/plms/s2-53.1.1)
Paul B. Yale, Automorphisms of the Complex Numbers, Mathematics Magazine Mathematics Magazine Vol. 39, No. 3 (May, 1966), pp. 135-141 (doi:10.2307/2689301)
MathOverflow, Wild automorphisms of the complex numbers
Created on November 15, 2020 at 05:21:40. See the history of this page for a list of all contributions to it.