EXAMPLE Metric tensor with $g_{\mu \lambda }=0$ for $\text{μ}\ne \text{λ}$, $g_{11}=g_{22}=g_{33}=1$, and $g_{44}=-1$ describes a flat pseudo-Euclidean space-time. 3D subspace of it for $\text{μ}\text{, λ}=1\dots 3$ is a flat Euclidean space.

Note 1 to entry: Special theory of relativity is based on the space-time described in the example.