In 1D case, R1 as a typical case of 1D Euclidean space is totally ordered. I was wondering if any 1D Euclidean space E1 is ordered as well? What is it
For higher dimensional case, are both Rn and En ordered? What are the orders?
Thanks and regards!
I meant for an order for an Euclidean space:
that can induce or be compatible with the topology of the Euclidean space;
or that is defined in their definition, for example, the order of R1 is the one defined in one of R1's definition as an ordered field with supreme property;
or that is used by default or most commonly.