Category:Definitions/Euclidean Space

This category contains definitions related to Euclidean Space.
Related results can be found in Category:Euclidean Space.

Let $S$ be one of the standard number fields $\Q$, $\R$, $\C$.

Let $S^n$ be a cartesian space for $n \in \N_{\ge 1}$.

Let $d: S^n \times S^n \to \R$ be the usual (Euclidean) metric on $S^n$.

Then $\tuple {S^n, d}$ is a Euclidean space.