•  
  •  
 

Article Title

Some Geometry of H(Rn)

Abstract

If X is a complete metric space, the collection of all non-empty compact subsets of X forms a complete metric space (H(X), h), where h is the Hausdorff metric. In this paper we explore some of the geometry of the space H(Rn). Specifically, we concentrate on understanding lines in H(R). In particular, we show that for any two points A, B, ∈ H(Rn), there exist infinitely many points on the line joining A and B. We characterize some points on the lines formed using closed and bounded intervals of R and show that two distinct lines in H(R) can intersect in infinitely many points.

Faculty Advisor Name

Steven Schlicker

Faculty Advisor Institution

Grand Valley State University

Suggested Mathematics Subject Classification(s)

51, 54

Comments

This paper was written while the author was an undergraduate at Grand Valley State University. The author would like to thank Dr. Steven Schlicker for all of his time, help and suggestions.

Included in

Mathematics Commons

Share

COinS
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.