TL;DR
This paper provides a pedagogical overview of maps between metric spaces, exploring Gromov-Hausdorff distance, its physical interpretation, and dilation structures as tools for understanding metric space mappings.
Contribution
It offers a simplified, educational presentation of complex concepts like Gromov-Hausdorff distance and dilation structures in the context of metric space mappings.
Findings
Clarifies the physical meaning of Gromov-Hausdorff distance
Introduces dilation structures as a simplification tool
Provides foundational understanding for metric space maps
Abstract
This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into another. See arXiv:1103.6007 for the context.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology