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It is proved that the Gromov-Hausdorff metric on the space of compact metricspaces considered up to an isometry is strictly intrinsic, i.e., thecorresponding metric space is geodesic. In other words, each two points of thisspace (each two compact metric spaces) can be connected by a geodesic. Forfinite metric spaces a geodesic is constructed explicitly.

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