For any metric space, the metric gives deep insight into the space such as geometry and topology of the space. Rather than directly
studying a specific space, one may wish to study a sequence of spaces with nice properties and then show that desired properties hold in the
limit. To study such a sequence of spaces, we use the Gromov-Hausdorff distance as a way to measure how close certain metric spaces are.
Along the way, studying the Gromov-Hausdorff distance gives a natural topology on which to show that set functions (i.e. diameter function,
measures) are continuous as well as tools to identify when the limit of convex sets is convex.

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