Completeness and Total Boundedness of the Hausdorff Metric

@inproceedings{Henrikson1999CompletenessAT,
  title={Completeness and Total Boundedness of the Hausdorff Metric},
  author={Jeff Henrikson},
  year={1999}
}
This paper defines and discusses the Hausdorff metric on the space of nonempty, closed, and bounded subsets of a given metric space. We consider two important topological properties, completeness and total boundedness. We prove that each of these properties is posessed by a Hausdorff metric space if the property is possesed by the underlying metric space. Finally, we explore applications of the Hausdorff metric, including fractal geometry. 

From This Paper

Figures, tables, and topics from this paper.
32 Citations
2 References
Similar Papers

Citations

Publications citing this paper.
Showing 1-10 of 32 extracted citations

References

Publications referenced by this paper.
Showing 1-2 of 2 references

Symmetry or Not?, The Mathematical Intelligencer

  • Kowohl
  • Symmetry or Not?, The Mathematical Intelligencer
  • 1998

Topology: A First Course

  • Munkres
  • Topology: A First Course
  • 1975
1 Excerpt

Similar Papers

Loading similar papers…