The Gromov-Hausdorff Metric on the Space of Compact Metric Spaces is Strictly Intrinsic

Understand

It is proved that the Gromov-Hausdorff metric on the space of compact metric spaces considered up to an isometry is strictly intrinsic, i.e., the corresponding metric space is geodesic.

• In other words, each two points of this space (each two compact metric spaces) can be connected by a geodesic.
• For finite metric spaces a geodesic is constructed explicitly.