Definition:Euclidean Space/Complex
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Definition
Let $\C$ be the complex plane.
Let $d$ be the Euclidean metric on $\C$.
Then $\struct {\C, d}$ is a (complex) Euclidean space.
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.
Sources
- 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $2$: Continuity generalized: metric spaces: $2.2$: Examples: Example $2.2.4$