0

if the topological boundary set is non-empty; we can put a field structure. for example 3-space is not a field but R^3-{Ox,Oy,Oz} is a field. i want to know can this be a theorem?

user117705
  • 1
  • 1
    Every infinite set can be given a field structure. The result you are mentioning, that $\mathbb R^3$ is not a field, essentially only says that there is no field structure which is compatible with vector space structure on this space. If you remove the axes, this statement wouldn't even make sense. – Wojowu Jan 08 '19 at 21:47
  • https://math.stackexchange.com/questions/3065885/turning-mathbb-rn-into-field – Asaf Karagila Jan 08 '19 at 22:08

0 Answers0