# Definition:Euclidean Space/Complex

< Definition:Euclidean Space(Redirected from Definition:Complex Euclidean Space)

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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 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 $2.2.4$