Definition:Euclidean Space/Euclidean Topology/Complex
Jump to navigation
Jump to search
Definition
Let $\C$ be the complex plane.
Let $M = \struct {\C, d}$ be a complex Euclidean space.
The topology induced by the Euclidean metric $d$ is called the Euclidean topology.
Also known as
The Euclidean topology, when applied to a real Cartesian space, is often referred to as the usual topology.
Also see
- Results about Euclidean spaces can be found here.
Source of Name
This entry was named for Euclid.
Historical Note
Euclid himself did not in fact conceive of the Euclidean metric and its associated Euclidean space, Euclidean topology and Euclidean norm.
They bear that name because the geometric space which it gives rise to is Euclidean in the sense that it is consistent with Euclid's fifth postulate.