2004 Student Research Conference:
17th Annual Student Research Conference

Mathematics and Computer Science

The Geometry of the Hausdorff Metric
Christopher C. Bay
Dr. Jason E. Miller and Dr. Steven Schlicker (Grand Valley State University), Faculty Mentors

The Hausdorff metric provides a way to measure distances on the collection of all non-empty compact subsets of real n-space. The resulting metric space is complete and has interesting geometric properties since it is a space in which the "points" are actually sets. It is of particular interest to fractal geometers. We examined the geometric properties of lines as determined by the Hausdorff metric and found that under certain conditions these lines are incomplete. That is, a Hausdorff line will not always have a full continuum of points in the sense that a Euclidean line always contains a full continuum of points. We characterize Hausdorff lines and determine exactly when these lines will be complete.

Keywords: geometry, metric, topology, lines

Topic(s):Mathematics

Presentation Type: Poster

Session: 26-23
Location: OP Lobby & Atrium
Time: 1:15

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