Completeness and Total Boundedness of the Hausdorff Metric
نویسنده
چکیده
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.
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