Category:Metric Space Completeness is Preserved by Isometry

This category contains pages concerning Metric Space Completeness is Preserved by Isometry:

Let $M_1 = \struct {A_1, d_1}$ and $M_2 = \struct {A_2, d_2}$ be metric spaces.

Let $\phi: M_1 \to M_2$ be an isometry.

If $M_1$ is complete then so is $M_2$.