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Some Geometry Of H(RN), Christopher Frayer

Furman University Electronic Journal of Undergraduate Mathematics

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 …